your screen is made of "gorilla glass". I had a screen protector on for a month and hated it, it got scuffed up and held dirt. When I took it off, the screen was way more responsive and hasn't shown an signs of damage. Been off for a few months now and I work in an auto repair shop, so it gets plenty of chances to gt messed up.
I fully believe it doesn't need one, but its up to you.