Doesn't it? What if they are fighting a knight who wears plate mail, carries a shield, and has a DEX of 15? Assuming that both the fighter and the guard have STR 16 (and so no bonus to hit), the fighter hits on a 19 or 20, the guard on a 20. That is twice the chance to hit!That distinction makes no difference to what I said. That 1 better to hit ACs 10 to 1 doesn't put the fighter head and shoulders above that guard.
Even against an AC 5 opponent (say, a guard sergeant wearing mail), the fighter hits on a 15+ (so 6 chances in 20), the guard on a 16+ (so 5 chances in 20). The fighter is 20% more likely to hit. That seems significant to me.