Tony Vargas
Legend
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).I will add though that if you're going to allow fighters to have them, then you may as well go ahead and let all characters have them. Fighters have access to the most feats...so it seems a bit pointless to limit players who would likely have less feats.
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.