Another way might be instead of +strength to damage break extra attacks into two abilities like so:I think this is mostly because many games never get to the point where fighters get a 3rd (or even 4th!) attack.
I agree that fighters are pretty good as is. I like the class personally, but I would still like to see something "combat" oriented to really set them "above and beyond" the other warriors in the combat pillar.
Quick thought: What if Fighters could make a weapon attack each round once they have Extra Attack, even if they didn't take the Attack action? If they take the attack action, they get their normal 2-4 attacks.
- Martial prowess At first level your skill with melee & ranged weapons is beyond compare. Rather than relying on brute strength & similar, each time you take the attack action against a single target you make a number of attacks equal to half your strength/dex mod rather than adding +STR or DEX to damage. Increase these attacks to half+1 & half+1 at level 10 & whatever
- Extra attack: At 5th level you make an additional set of attacks whenever you take the attack action at a -2 penalty This set of attacks can be against the original or a second target within reach. This scales to a third set of attacks at +4 at level 10 & 4th at - whenever.