I have an iPhone 13 Pro. I came from an 8 Plus which was LCD, and I thought I wasn't going to be able to tolerate the 13 Pro. But I use an Armor Shield (think of it as Skinomi Tech Armor reborn, even though it isn't the same company) and once that was on the phone, it's been absolutely fine. No problems at all.
So yes, the screen protector can make a world of difference.
I am debating getting a 16 Pro Max from AT&T (which I can return) and testing it out. Need to make sure it can go back if I hate it.