You all know that screen protectors are a left-over technology from the days of plastic screened devices like the Palm Pilot etc?
With tempered and chemically treated glass screens, (Gorilla etc) it is almost impossible to scratch the surface without really trying to. Why do you suppose all mainstream OEMs went to glass screens? Just to sell more replacement screens after breakages? Why do you suppose the mainstream OEMs make the screen-layers glued to the glass? Just to sell more screen assemblies after breakages?
Some low cost phones still use plastic and a protector would be useful there, but with glass screens, you are just paying for something that is not needed. The "protector," will not aid saving the screen from physical damage like dropping it or dropping something hard and heavy on the glass.
Save your money and the effort to put it on rather than letting the Urban Myth prevail? If physical damage protection is a desired option then buy a bumper-style case.
Fun fact Palm PDA's used both glass and plastic digitizers depending on time period and cost.
While today's glass is an improvement, its not as scratch-proof as you say it is. My 920's glass disagrees with your claim, and I'm sure many others will agree. I went naked early on in my ownership and a klutz of a friend dropped it a couple feet where it slid on the ground. Result: Three nasty scratches across the back button, the right and left side. (ignoring the tiny ones that appear from normal use)
Of course, plastic film protectors only protect against scratches and not shatters, but the glass on my 920 which unfortunately broke a little while ago actually is held together quite well by the protector - smoothes over the cracks too. itssomething.jpg
However, I've heard of some cool thing called tempered glass screen protectors which take the force of a drop and crack so the main screen its protecting doesn't have to. Haven't tried one personally, but it sounds cool.