That actually isn't my point. I don't believe the base 5e fighter needs any "fixes" at higher levels.
I dont think its matter of fixing its power output. Its more the versatility of the class and its ability to shape the narrative that is lacking. Sure a skilled roleplayer can manage a few good things in therm of setting influence, but every character as access to skills, so its not really a matter of classes.
I agree that in 5e the fighter is mostly fine, but a little bit restricted at higher level. But that in ''basic'' 5e, with more or less no rules for social combat, journey, retainers, stronghold etc.
If A5E is to add those extra systems, the fighter will feel really lacking, because his only options to interact with those systems will the the same skill checks as anybody else. Meanwhile, the Ranger will be rocking the journey rules, the spellcaster will be sprouting fortresses, temples, groves etc left and right, bard will be gathering small armies of retainers with the CHA expertise and mind affecting spells etc.
I dont know if I express my point clearly? In short the fighter is ok with is limited role in a system with little to no breadth or depth, but if you create a new game with a goal of adding more depth to rules, the fighter will be left in the dust by the other classes.