I can't remember if I already posted this on here or not, but I was in a motorcycle accident 2 years ago and my iPhone5 was expelled from my front pocket at 40mph and skidded across the pavement. A good Samaritan grabbed it for me and gave it to the paramedics. I'm still using the phone to this day, not a scratch on it... though the battery is completely done and the phone randomly shuts off.
I remember those old clamshell flip phones external displays used to get pretty scuffed up, but that was before they started using materials like Gorilla Glass. I've never seen a smartphone with a scratched or scuffed screen. Smashed? Yeah. But not scratched.
Long story short, I think screen protectors ruin the intended touch experience and look of the device, so I don't use them. On that same note, screen protector technology has come quite a long way over the years and they're much better and clearer now than they used to be. The one the AT&T store put on my fathers iPhone6S is hardly noticeable, and is crystal clear.