I think screen protectors help to some extent in protecting the screen from scratches and possible breakage. Also saw less fingerprint smudges on my iPhone screen with the protector on it. Got a case last year which also came with a screen protector, but didn't like it that much. It started to peel off from the edges within no time, then someone told me about this rather unknown brand, HAGZ Screen on Amazon. Got one and have been using it since late last year without any issues yet.
Hope you're not trying to use one as a condom.Screen protecors are like condoms.