QUESTIONS:
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?
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?
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.?
4. Could hit dice be gained in ways other than by leveling, such as a magic item?
5. Could a creature or character have more hit dice than its level?
That's it for now. Of course I have my own views on all of these questions, but instead of potentially biasing responses by putting my own thoughts down at this time, I am curious to hear your thoughts on the questions.
Thanks to all who take the time to reply, it is much appreciated!
ANSWERS.
1. Because it's a game. Spellcasters get lower HD for balance reasons. Characters who are more likely to take damage (fighters, barbarians, clerics, etc.) get higher HD. From a diegetic perspective, the barbarian is a savage fighter who is adept at turning potentially-lethal attacks into near misses.
2. Because it's a game, and people like class differentiation. You can give size-based HD if you like--and I do like, but I like race-as-class so would be inclined to create a Man class, an Elf class, a Dwarf class, and so on to accompany this--but it will alter the mathematics of the game. Dropping it willy-nilly into 5e will cause some issues.
3. Because it's a game, Dexterity already does too much, and bloating hit points more with additional modifiers is a poor idea.
4. Yes, but why would you confuse the system like this? If Sam wields the One Ring, sure, he fights as a 6 HD fighter, but when he takes it off, he's back to being a 2 HD halfling...but that introduces all sorts of mathematical weirdness into the mix, so why bother?
5. Not in 5e. But there are esoteric editions in which monsters have no level, only HD.