That's not remotely how I build a character but just to go along with it. Now you have two max stats, lets say str and con. Then what? You still have 9 points to spend on stats purely for skill/save use. You saying dex is bottom of the list? Stealth, initiative, dex saves, acrobatics, rope use are all useless? Personally I think you are over rating Con. My Con 12 fighter is doing just fine.
My first 5E PC was a single class vuman fighter, Str 8 Dex 16 Con 12 Int 8 Wis 13 Cha 16. I'm quite happy to do without max Con for a warrior, but putting points in Str would be a waste while points in Con, Int, Wis and Cha all have their uses. I'd like higher stats in all of those four, but y'know, point-buy.
I knew I wanted the best possible attack stat, and since my concept was a dextrous, charismatic swashbuckler I wanted a high Cha, and valued that more than high Con. He wasn't min/maxed because Cha doesn't make him a better melee combatant; I just wanted a PC who could do stuff outside of combat as well as in combat. I was very pleased that I could still have a high Cha without gimping my warrior. I could've focused on Int instead, but point-buy means something has to give. Putting points in Str would have so little benefit; skills? Only Athletics, and I had Acrobatics. Saving Throws? Str is an uncommon save, and I'm proficient anyway. Compare that to the skills available for the mental stats. You'll note the odd Wis score; my plan was to take Resilient-Wis later on.
Point-buy affects how you make your PC. If you have rolled six scores, you can arrange them how you like, and I would've arranged those rolls in order, Dex first, Cha second, then Con/Wis (saving an odd score for Wis if possible) and then Int and lastly Str. However, if I had rolled, say, 11 as my lowest score and assigned it to Str, then that is that! I couldn't make myself weaker in order to be more charismatic than my roll of (say) 15.
But point-buy lets you do that! And the scarcity of points combined with no need for
two attack stats leads to an evolutionary pressure in point-buy to have 16/8 or 8/16 in Str/Dex (for a non-barbarian warrior), and any other use of your points is foolish.
How about a ranger who uses twin axes?
I'd either start with a level of fighter for heavy armour proficiency, Con saves to aid my concentration checks, and a second fighting style....or I would choose shortswords so I wouldn't have to waste points.
If I attack with Str but can't wear heavy armour, then I start with Str 16 and Dex 14, leaving me with both stat bonuses used and 13 points left; the best starting medium armour gives me AC 13 + 2 from Dex = 15.
If I used shortswords then my Str is 8 and my Dex is 16, leaving me with one vuman bonus point and 18 build points. My starting AC is 12 (studded leather) + 3 Dex = 15. Same AC, same +3 to attack/damage, less weight, more starting money left, more points left for better Con and mental stats.
Or a rapier and bow using elven fighter who wants to wear heavy armour?
AC = 16 (splint); one more than studded leather plus Dex at the cost of 5 build points wasted on Str instead of spent wisely on the other stats, more money, more weight, disadvantage on Stealth. Or I might have Str 8 and take the encumberance penalties.
The point of heavy armour isn't just for the pleasure of saying you wear heavy armour! The point of armour is to have a better AC wearing it than you would have
not wearing it, without gimping you too much in other ways.
A great weapon using paladin that wants to be stealthy.
My second PC was a Pal 2/War 3 (fiendish chainlock) in
mithral full plate and,
despite his Dex of 8, proficient in Stealth. Problem with heavy armour: poor stealth. Solution: mithral armour removes disadvantage, Stealth proficiency results in Stealth +2 at 5th level. Not the best, but certainly good enough for a guy in full plate!
Are these characters all not viable? I am playing two of these and can say that I believe they are, since I am having fun and that they are still alive.
I enjoy making PCs that
seem as though they have gimped themselves but who have solved their own problems. The Pal/War mentioned above, my Bar/War who cannot cast (or concentrate on) spells while raging, but who uses her two slots to cast
armour of agathys and one pre arse-kicking
fireball before going postal, knowing AofA will last twice as long because she takes half damage while raging.
In the end, I think we both agree that
the most important thing is that we think our own PC is cool! We just have to make it work; play to our strengths and minimise our weaknesses. It's just that I cannot justify spending build points on
both attack stats when making a non-barbarian warrior. It gimps me for no benefit in return.