I've managed to scratch every screen I've not had a protector on (although I tend to buy less expensive phones, even my Nexus 6 managed to get scratched.)

Also, I prefer a non-glossy screen. Basic plastic anti-glare protectors are super-cheap (3-5 for $6-8), and protect from scratches, at the expense of picking them up like crazy themselves. It's not a big inconvenience to swap them every couple of months.