Not if you use decent quality tempered glass screen protectors. Mine has been on my current iPhone well over a year and you wouldn't know it has a screen protector on. The touch is also just as responsive, if not a bit better as the bare screen is a bit more grippy to the touch. The days of screen protectors being tacky plastic films are thankfully over.
I've always used screen protectors but recently have been using my 15 Pro Max without a case. So now am thinking of going all the way and removing the screen protector. It's been so long that I've now had a screen protector on I don't think my fingers have touched an iPhone screen for 15 years or so!!! Still not read through all of this thread yet so we'll see....
I've had my screen crack once from a fall -- it didn't have a screen protector on it.
Now, a screen protector is placed on day 1. It's been 11 generations (I've skipped a few) with 0 issues with many broken screen protects but perfect screens.