A screen protector only prevents the screen from getting scratched. It will also help hold a broken screen in place once shattered. A screen protector will not prevent your screen from breaking if dropped! If your phone gets dropped and hits the floor at just the right spot, your phone screen will break. Don't drop your phone and your screen won't break lol
In the 26 years I have been using mobiles, I have broken none and I have never purchased a screen protector in my life.
Well you have been very lucky in not breaking a screen
Screens are thin and there is nothing strong or sturdy about them. Have you ever held a replacement screen in your hand? As someone else said, glass is glass...
I keep my phones in a leather foldable case and so it has maximum protection when/if dropped. No guarantees of course, it's all about how it lands (like you said).