Not sure your age, but do you remember the Aria RPG from the early 90s? It was a very cool concept with a clunky system, but some interesting elements. Characters had tons of ability scores - can't remember the number, but I think over 10. For most skills you could choose from a number of attributes to create your modifier. Meaning, the system acknowledged that very few actions (skills) involved only a singular attribute, or even way of doing things.
So for instance, a sword-wielder didn't have to use only strength or dexterity, but could use intelligence or perception - or some combination (again, I can't remember the details and am too lazy to dust off the book and do the research).
Obviously that doesn't totally translate to D&D, if only because D&D only has six ability scores. But I think the general idea could be employed. For instance, maybe a broader Finesse rule that gives all weapons minimum STR and DEX; if you're above those, you can use either ability score, or even INT or WIS, or a combination of the four (Say, the average of two).
So for instance, let's say the minimums for greatsword are STR 12, DEX none. Let's say you have a character with a STR 12, DEX 15, INT 10, and WIS 14. This character was trained in a blade style that is focused more on speed and perception, so because they meet the minimums, they can use their DEX/WIS combination to get a +2 to hit and damage, rather than STR.
I'm just thinking out loud here. Maybe this doesn't work or over-complicates things. But it does open the door for players to create more specific character concepts: e.g. a quickness and perception based fighting style, that isn't focused on brute strength, even with a heavy weapon like a greatsword.