Faster does not mean better. It just means faster. And fighters aren't punching a thousand times. They're punching two or four times. I can flail around a lot, but I certainly wouldn't hit very often. More opportunities to hit isn't the same thing as being skilled at hitting, because it means they have more opportunities to miss as well.
As I said, fighters should both be better at attacks (such as by a weapon specialization ability, or by getting a nonmagical +1 to attack rolls at a certain level, or by extending the crit range at a certain level) and have multiple attacks per round. This isn't an either/or thing.
They "can," but they don't, because the attack bonus isn't any better. Rogues and monks both have Aim abilities--rogues can't move while Aiming, and monks have to spend ki--and that, I feel, does a much better job of representing skill than just being fast at it. Why not give fighters something similar? When they use their Extra Attack, if they make all attacks on a single target, then the last attack is made at advantage. This represents them studying how their foe is moving on that turn.