I put a protector on mine and it works flawlessly. I'm careful with my electronics, but my rule is that if I'd "cry" over a scratch or any other cosmetic damage, it gets a screen protector and a case.
My phone on the other hand, is a painfully cheap feature phone. I've been plotting its death for years, never put it in a case or used a screen protector, and the D#%$ thing still works perfectly. It's just taunting me, knowing how much I don't like it, but I just can't justify buying another one until this one breaks!