You could make an argument for screen protectors minimizing scratches, but of course the protector itself still gets scratched and still looks lousy.
As far as “breakage” protection, don’t bother. The “protector” is FAR more fragile than the actual screen, so it’s going to break in conditions where the screen wouldn’t. And if you impact the phone enough to ACTUALLY break the display, that flimsy film ain’t gonna matter.
I didn’t vote because you don’t have “No, because it’s useless” as an option 😉