Tony Vargas
Legend
Systems can and have gone there with reasonable results. Back in '78 RQI calculated your chance to hit with modifiers from high STR, SIZe, DEX, INT, & POWer. Everything but CON, IIRC.There is more to the game than just to-hit and damage rolls. And "every fighter has 20 str" is not a great world building.
But... Maybe you'd like something like...
To-hit: Wis+Cha+Dex
Damage: Str+Con+Int
FWIW, 5e BA has already tried to decrease the impact of high stats, both with the cap of 20, and putting everyone on the same proficiency schedule.