DND_Reborn
The High Aldwin
Again, my thanks to all for their responses. I am going to now answer my own questions, somewhat in response to many of the responses. Some points of course will be for further discussion, others are just my ideas. 
A sorcerer, and other casters, would have a greater opportunity to be engrained against damage that is not related to weapons, claws, etc. If I was a sorcerer, planning a life of risk and adventure, I would work to endure myself to magical hardship as well as any physical I could. If I had a "training partner", who could target me with a magic missile (painful, but not lethal), I would be able to build up my tolerance for such injury.
Also, who is to say my sorcerer did not grow up in a harsh environment. Perhaps, as a "nerdy wizard type" I was beaten up often growing up? I would certainly learn how to take a punch and deal the the physical pain as well over time.
My point is damage, as a singular measure, encompasses many types of threat or injury. Barbarians would likely be superior to some of those, but I think other classes would be better against other types of damage. Overall, if we look at everything we can when considering the abstractness of hit points (and thus hit dice), I really don't see any reason why some classes should have a larger hit die than others.
I like some of the suggestions about representing the barbarian's "toughness" in other ways via game mechanics. I don't think hit dice and hit points are they way. Also, the already present rage feature and resistance to BPS damage effectively nearly doubles their hit point potential when mitigating most damage.
Increasing the hit dice to d6 for small, probably adds up to another 2 "meats" hit point, again the remaining from abstract sources.
On to d8 for medium creatures, and we add another up to 2 "meat" hit point. At this point, up to 5 hit points represent "body", other hit points are skill, luck, divine favor, reflexes, etc.
The pattern is thus that a maximum of up to 3 hit points per die (regardless of die size) should be abstract, the remaining potential is "meat" hit points. I believe this makes sense because the other abstract factors of hit points (again, skill, luck, divine favor, etc.) really have NOTHING to do with a creature's size.
I am not opposed to thus following the idea the creature (and character) size indicates hit die size. Smaller PCs could have a d6, and perhaps have some other mechanical benefit to offset it (perhaps a +1 to AC, or something, but that is a separate issue). Or, given the nature of PCs, you could easily support that small-size PCs also use a d8 due to their "heroic" nature. Personally, I wouldn't and do not like that solution, and would rather find some other means to support small-size PCs so the loss of hit points is balanced out.
At any rate, I've argued in other threads about other ability modifiers representing bonus hit points, so I obviously I have no issue with other ability modifiers being used. For a very long time in 5E, we've played you add your highest ability modifier to hit points, not necessarily Constitution.
I don't buy the argument made by some that Constitution is not really needed (I've been through this debate, and although I can understand their points, I just happen not to agree with it). What does bother me is that by linking it to hit points, only 2 PCs IME (not even my PCs) out of the 50 or so I've seen played have a Constitution of less than 12 (both PCs had 10). IME this makes CON usually a 2nd or at worst a 3rd best ability score. Most PCs IME have CON 14 as a minimum simply because they want the extra hit points!
So, but instead linking hit points to your highest ability modifier, this issue is removed. Now, immediately you might think this would increase hit points incredibly, given most PCs start at +3 or +4 as their highest ability modifier, and reach +5 quite often, BUT we only add this at 1st level, not at every level! Due to this, PCs actually have fewer hit points than RAW.
As others have mentioned, I agree there are too many hit points in 5E (the dreaded "bloat"). By removing CON bonus hp, and adding the highest ability modifier, we've removed a lot of the problem (in PCs and creatures, alike).
Also, to be more clear, I mentioned gaining hit dice, not hit points. Older edition potions (heroism, etc.) added hit points, along with the bestowed energy levels. Since older editions only used hit dice to add hit points, it isn't quite the point I was making.
So, I should have been clearer. My bad.
What I meant was gaining bonus hit dice due to a feature or feat maybe. A magic item could also do it. Although limited to healing, spending these bonus hit dice could allow the PC or creature to heal itself (essentially).
I asked this because my thoughts about removing hit dice from leveling, but grant them in other ways maybe. I do think something like magic armor that granted hit dice (for healing after a short rest in RAW) would be cool. But, we've been exploring other uses for hit dice, so gaining them in a fashion other than leveling could work for those uses.
The idea also is to decrease hit point maximum, but allow for more "recovery" during the adventuring day. For example, in RAW an 8th level Fighter with CON 16 would have 76 hit points. Let us assume the Fighter has a highest ability score maximum of +4 (probably STR or DEX), and remove the bonus HP from CON. This would reduce the PC to 56 hit points. Even with fewer hit points, such a PC could take several hits in a combat and really not be too concerned. Large damage sources would be of greater concern, however.
On the even levels, the PC would gain an extra hit die (2 total at even levels). Now the PC would have 12d10 hit dice (not 8d10). After a fight, with so many hit dice, the PC can rest and recover the abstract hit points more often.
This makes individual encounters more dangerous, but overall survivability would still be decent. You can see in the table below that if all the hit dice were spent during an adventuring day, the total available HP would be roughly the same.
Anyway, that was some of my thoughts that prompted the OP. I am curious as to your views. Again, thanks for any replies.

Many people argue that warriors have larger HD because they are used to the rigors of life and/ or combat. If damage was solely physical, I could understand and agree with this. But damage isn't in 5E. It is often force, radiant, necrotic, psychic, etc., and often even the physical sources are magical in nature.1. Why would a barbarian earn a d12 for hit dice, while a sorcerer gains only a d6? What is the reason why some classes have larger hit die types than others?
A sorcerer, and other casters, would have a greater opportunity to be engrained against damage that is not related to weapons, claws, etc. If I was a sorcerer, planning a life of risk and adventure, I would work to endure myself to magical hardship as well as any physical I could. If I had a "training partner", who could target me with a magic missile (painful, but not lethal), I would be able to build up my tolerance for such injury.
Also, who is to say my sorcerer did not grow up in a harsh environment. Perhaps, as a "nerdy wizard type" I was beaten up often growing up? I would certainly learn how to take a punch and deal the the physical pain as well over time.
My point is damage, as a singular measure, encompasses many types of threat or injury. Barbarians would likely be superior to some of those, but I think other classes would be better against other types of damage. Overall, if we look at everything we can when considering the abstractness of hit points (and thus hit dice), I really don't see any reason why some classes should have a larger hit die than others.
I like some of the suggestions about representing the barbarian's "toughness" in other ways via game mechanics. I don't think hit dice and hit points are they way. Also, the already present rage feature and resistance to BPS damage effectively nearly doubles their hit point potential when mitigating most damage.
This is the way I am leaning. If we concentrate on the "meat" hit points, a tiny creature with d4 hit dice might have just 1 "meat" hit point. Any additional hit points is from the other more abstract sources.2. Medium creatures use a d8. Most PCs are medium in size, so why not give them the same d8 for hit dice? If we did, would it be too harsh on small characters to give them the d6 small creatures gain for hit dice?
Increasing the hit dice to d6 for small, probably adds up to another 2 "meats" hit point, again the remaining from abstract sources.
On to d8 for medium creatures, and we add another up to 2 "meat" hit point. At this point, up to 5 hit points represent "body", other hit points are skill, luck, divine favor, reflexes, etc.
The pattern is thus that a maximum of up to 3 hit points per die (regardless of die size) should be abstract, the remaining potential is "meat" hit points. I believe this makes sense because the other abstract factors of hit points (again, skill, luck, divine favor, etc.) really have NOTHING to do with a creature's size.
I am not opposed to thus following the idea the creature (and character) size indicates hit die size. Smaller PCs could have a d6, and perhaps have some other mechanical benefit to offset it (perhaps a +1 to AC, or something, but that is a separate issue). Or, given the nature of PCs, you could easily support that small-size PCs also use a d8 due to their "heroic" nature. Personally, I wouldn't and do not like that solution, and would rather find some other means to support small-size PCs so the loss of hit points is balanced out.
Luckily, Constitution is not just "meat" hit points. The ability to withstand pain and injury, as well as general health, also contribute to the abstract elements of hit points. Certainly, a CON bonus could be "meat" hit points, but it isn't necessarily. Given my points above, personally I like to think that maybe just 1-2 bonus hit points from CON would be "meat" at most, any additional CON bonus would be more abstract.3. Due to the metaphysical or abstract nature of hit points, why is only the Constitution modifier used? Would the other abilities represent other abstract aspects of hit points, such as Dexterity representing the reflexes aspect, equally well? What about Wisdom or Charisma representing divine favor or luck, etc.?
At any rate, I've argued in other threads about other ability modifiers representing bonus hit points, so I obviously I have no issue with other ability modifiers being used. For a very long time in 5E, we've played you add your highest ability modifier to hit points, not necessarily Constitution.
I don't buy the argument made by some that Constitution is not really needed (I've been through this debate, and although I can understand their points, I just happen not to agree with it). What does bother me is that by linking it to hit points, only 2 PCs IME (not even my PCs) out of the 50 or so I've seen played have a Constitution of less than 12 (both PCs had 10). IME this makes CON usually a 2nd or at worst a 3rd best ability score. Most PCs IME have CON 14 as a minimum simply because they want the extra hit points!
So, but instead linking hit points to your highest ability modifier, this issue is removed. Now, immediately you might think this would increase hit points incredibly, given most PCs start at +3 or +4 as their highest ability modifier, and reach +5 quite often, BUT we only add this at 1st level, not at every level! Due to this, PCs actually have fewer hit points than RAW.
As others have mentioned, I agree there are too many hit points in 5E (the dreaded "bloat"). By removing CON bonus hp, and adding the highest ability modifier, we've removed a lot of the problem (in PCs and creatures, alike).
I just I shouldn't have used the "magic item" as the example because people seemed to focus on it. shrug4. Could hit dice be gained in ways other than by leveling, such as a magic item?
Also, to be more clear, I mentioned gaining hit dice, not hit points. Older edition potions (heroism, etc.) added hit points, along with the bestowed energy levels. Since older editions only used hit dice to add hit points, it isn't quite the point I was making.
So, I should have been clearer. My bad.

What I meant was gaining bonus hit dice due to a feature or feat maybe. A magic item could also do it. Although limited to healing, spending these bonus hit dice could allow the PC or creature to heal itself (essentially).
I asked this because my thoughts about removing hit dice from leveling, but grant them in other ways maybe. I do think something like magic armor that granted hit dice (for healing after a short rest in RAW) would be cool. But, we've been exploring other uses for hit dice, so gaining them in a fashion other than leveling could work for those uses.
Again, this is linked to the idea that hit dice are used to recover following a short rest.5. Could a creature or character have more hit dice than its level?
The idea also is to decrease hit point maximum, but allow for more "recovery" during the adventuring day. For example, in RAW an 8th level Fighter with CON 16 would have 76 hit points. Let us assume the Fighter has a highest ability score maximum of +4 (probably STR or DEX), and remove the bonus HP from CON. This would reduce the PC to 56 hit points. Even with fewer hit points, such a PC could take several hits in a combat and really not be too concerned. Large damage sources would be of greater concern, however.
On the even levels, the PC would gain an extra hit die (2 total at even levels). Now the PC would have 12d10 hit dice (not 8d10). After a fight, with so many hit dice, the PC can rest and recover the abstract hit points more often.
This makes individual encounters more dangerous, but overall survivability would still be decent. You can see in the table below that if all the hit dice were spent during an adventuring day, the total available HP would be roughly the same.
Anyway, that was some of my thoughts that prompted the OP. I am curious as to your views. Again, thanks for any replies.
