I'm pretty careful (rarely drop my phone, and keep it in a pocket where I never put anything else), and in my 12 years of using glass smartphone screens without screen protectors (6 of those years without a case either), I've only ever gotten a noticeable scratch once (on my iPhone X, from the metal corner of my iPad cover), and it was only noticeable with the screen off or in really bright lighting. That said, I keep my phones a lot longer now (3 years) than I used to (3-6 months lol), so for my 14 Pro Max, I decided to use a screen protector for the first time. Actually, I started 3 months ago with my 12 Pro Max because I was going to climb Mt. Kilimanjaro and was worried I would scratch my screen there, and I noticed so little difference that I kept it on until my 14 Pro Max, even though I had intended to take it off after the climb.
TLDR: It's very possible to use a phone without a screen protector and never get a scratch, but, if you have a screen protector, you don't have to be as careful and you also have nice peace of mind.