Not allowing ASIs seriously hinders characters that rely on Dex for AC like Light Armor, Mage Armor, Natural Armor classes. I know it's not a total game breaker, but I think you'd see a lot more feats used to squeeze into Medium armor and Shield.
There are still a lot of feats that are good on any character like Alert, Mobile, Lucky, Resilient, Magic Initiate, Tough, Skilled, Healer, and even Observant.
I've played in a party where we all got Mobile for free at level 1 and it was fun. It'd also be fun if everybody had Alert. Most combats would FEEL like a surprise round.
I do agree though that the half feats that give a +1 to something would be more popular that ever. Especially the Armor Feats. Suddenly, it'd be worth it for a caster to taker both Lightly Armored AND Moderately Armored for the +2 Dex and the much higher AC. Every single Heavy Armor guy would want Heavy Armor Master. Every single build would have Resilient.