This isn’t a rules suggestion – at least not yet. I was just thinking that with a focus on multiple attribute dependency, embracing the strategy that characters will need to have multiple high stats to get the most out of any particular role, you could provide some useful and fun differentiation in . . . well, lots of things.
Note that I’ve not canvassed even the DMG, and certainly not Sage Advice or any sort of alternate rules books for these. I’m just free-associating. So I may well be reinventing a bunch of wheels here.
Certain weapons could be more challenging to use than others, providing a DEX-based penalty to hit. This would be overcome by proficiency and stat bonuses.
Weapon size and reach could impact initiative. So smaller weapons would provide a boost to initiative, large ones a penalty, relative to STR. While it might be a bit odd, one could only use penalties to initiative, so that a guy of any STR who is punching or using a dagger just uses the system as written – DEX bonus and that’s it. But if your STR was lower than the modifier for the weapon (so at low enough STR, even a human-sized dagger might be slow) you take a penalty.
STR already impact weapon damage straight-up, and under a MAD system this would not change, though it might be that large weapons, which already get boosts to raw dice of damage, require being over the STR rating to get damage bonuses. Not sure about this one, though. Each additional die rating (d6 to d8 to d10) is basically a +1 to damage anyway, so saying “sure, a greatsword is 1d12 or 2d6, but you can only wield it effectively if you’re higher than STR [whatever]” would hit both damage output and weapon speed. Probably too much.
That being said, it’s easier to say “hey, if you’re not strong enough to draw back a bow, it’s both slowr and double-dips for damage.” That’s actually not wrong, since half-drawing a bow quarters the energy in an arrow. Still, one mixes physics with D&D at great peril. It’s not that kind of game (and that’s OK).
I like the idea of bows having a STR rating, basically a draw weight. A very strong bow might be a STR 18 or even STR 20 bow, good for +4 or +5 to damage. But you couldn’t use it at STR 16. or you could use it, but it makes you tired, or you take a penalty to your hit roll, reducing your odds of a successful damaging strike, or even just roll at disadvantage, which is much more in keeping with the “don’t sweat the penalties” philosophy of 5e.
To do this right without it being a giant NERF ME button, it would have to be pretty much a top to bottom look, with eyes to more than just the fighting classes. If you need to have great STR, DEX, and CON to be a good warrior, with INT, WIS, and CHA also being useful, you’re going to want to make sure that (for example) DEX, INT, and CON are important for spellcasters, with STR, WIS, and CHA also being useful. That sort of thing. Even beyond skills, every class needs to derive benefit in their primary roll from every stat in order for this to really work.
Otherwise, nerf bat. Ooops.