I used my iPad 2 without cover and screen protector, and the screen is still fine, even after those years. I also use y iPad Air 2 without a screen protector, though I did get a transparent back cover for it that has a good grip. The front/glass are uncovered, however. No scratches at all.
My reasoning is that the screen is beautiful and all protectors I have seen or tried (even on smaller devices) take away from that beauty. At the end of the day, it's also a tool, not a collectible. It doesn't need to stay in pristine conditions (I have stringed instruments that are far more valuable than my iPads, and I don't cover them with a protective film either!) But really, I think you have to be deliberately careless or unfortunate to scratch the screen of an iPad.