For me, a phone is a necessary tool, not a precious artifact. It gets treated like any other tool, not packed in cotton wool. It's an electronics device with a finite life-span, not an objet d'art.
I sometimes, in a rush, put my phone in my pocket with my car keys. Or it slides down the side of my car seat and gets jammed in there. Or I unexpectedly get gritty sand in my pocket while at the beach, and throw my phone in there with it. Or it gets knocked of a table by some careless colleague. No big deal.
So, there are two choices - add some extra protection, or just put up with any damage that eventuates. I opt for the former. I don't find cases or screen protectors offensive (in fact, I can't stand camera bumps, so a case to flatten the back is mandatory).
That said, even with all that mistreatment, I can't see a blemish on my current phone, its case, or its screen protector. However, if it did get scuffed, it's a quick job to replace the screen protector and restore a pristine screen.
Screen protectors serve a purpose for many of us. But of course they will reflect light if not AR-coated. I can't imagine how anyone would be confused about that.