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Disagree, D&D is not really a D6-centered game compared to many others. I remember a lot of the sense of wonder when I first rolled a d4 or a d12 ...(hmmm, what weapon does THAT damage??). haha. in D&D, I don't remember many weapons doing more than d10, which is what a 2handed sword did.
Just wanted to say, I really enjoy reading the perspectives here, and I wish that, ideally, a 20th level monk is using Dim Mak and Quivering Palm maneuvers, and you are all broken inside, stunned or disabled, but don't realize you are dead until a round or two later, and a 20th level fighter just chops you in half. Same end result, different ways of going about it.
Two handed weapons just need to be the ultimate in damage dealing in D&D again, for most normal dungeon scenarios. Once you're using Lances or Polearms from a mount, that's something else entirely.
But if I do ever get that 29-strength belt of Storm Giant strength, I do NOT want it to just mean I cannot miss except on a natural 2 or less. I want to be a fearsome sight, lifting a table with 5 orcs on it and throwing the whole thing into the pit, I want my sword to cut that IRON GOLEM in half, I want my warhammer to knock enemies left and right out of my way, Sauron-stylez.
You cannot do that sort of stuff with just a to-hit bonus. Needs a damage bonus and perhaps some maneuvers like "Throw enemy" depend on your strength mod and their weight. I do not want some "power" in a martial-themed character who does not use magic, to overcome the fact that he has 8 strength but stilll says "you knock your opponent back 20 feet".
I did martial arts for many years and know it's not just your weight, but your ability to deliver explosive bursts of strength, in say, a shuffling side kick to push your target back. But key word there : strength. A smaller / weaker monk would NOT be using that kind of northern style show of force, they'd be doing internal styles that focus on attacking pressure points or sensitive areas to "crit" instead.
The big brutish barbarian hordes lost out despite vast size differences and far greater numbers to roman soldiers, due to training, discipline, and smart choices of gear. But one on one is not the same, and the romans used Germans for the Praetorian Guard for a reason. Because they were big, scary-lookin' mofos that you didn't mess with, like twice the size of the average roman. Very intimidating. So the huge guy who focused on his strengh might win smaller battles, but larger ones requiring tactics and coordination and discipline would favour those with better training.
My point is : I want D&D to mimick and allow both of those biases in combat. And yeah, the big brutish guys would use bigger weapons for a reason. Definitely to take advantage of a larger strength mod bonus to damage
D&D rules adding a min and a max str mod per weapon, would allow this, and is not calculated each round, just written down once on your character sheet and bam, done.