FormerlyHemlock
Hero
The whole point is to give fighter something unique, and to keep feats mostly off the table for simplicity elsewhere (fighter is the simplest class).
Though, to further keep a lid on it, maybe they could only take Feats with their two 'extra' ASIs, at 6th and 14th. And/or limit the feat option to the Champion, specifically.
edit: Oh, the OP should also decide if Fighters can be variant humans and get that feat at 1st level. Shades of 3e, there.
That was the OP's proposal: fighters only get to use their 6th/14th level ASIs on feats.