I didn't run one on my Pixel XL (which my Note 8 is replacing). My Pixel doesn't have a single scratch on the screen. Ironically, I did scratch the hell out of the rear glass and I believe I did it while trying to apply a screen protector to the front. Normally I place my phone on a microfiber cloth or something soft while putting on a protector, but this time I laid the phone right out on the counter. I believe the scratches to the back happened while I was trying to press down on the sides of a tempered glass screen protector to get them to stick down. I was unsuccessful, so I ended up tearing the protector off (and going without). I was left with the scratches to the rear glass as a reminder.
I'm thinking of going without a screen protector on the Note. I've heard too many issues with tempered glass screen protectors (which I prefer) and curved phone screens. I kinda learned this with the Pixel XL, which does have curved edges on the perimeter (though not as pronounced as Samsung phones with the edge display), as I tried to apply multiple tempered glass protectors to it but couldn't get the edges to stay down resulting in a halo effect.
The complaints I hear now are that a lot of the tempered glass protector manufacturers are only putting adhesive on the edge to try to combat the problem with them not sticking down. This means the center is not adhered to the screen, leading to reduced touch sensitivity. This makes the Whitestone Dome Glass seem like the only one worth getting but I'm not sure if I want to drop $50 on it, especially with the risk that it will interfere with a case.