It's currently Gorilla Glass 3 (which is harder than Gorilla Glass or Gorilla Glass 2) - which has a hardness of 5-6. As opposed to the hardness of carbide at 9. Scratching Gorilla Glass 3 with carbide is about like scratching window glass with diamond. Your nails can't do anything to Gorilla Glass, neither can most metals. But a sub-micron size particle of carbide? It makes melting through butter with a white hot wire seem difficult. It's why people who wear glasses are told to NEVER wipe them dry - you wash the particles away with the spray, then wipe the grease off with the wet tissue. You can't spray a phone screen (if a drop of liquid gets inside the phone, it's going to slowly corrode and destroy the phone), but you can dampen a tissue with lens-cleaning solution and use that to remove fingerprints. Otherwise you're just smearing them all over the screen. (The part of the glass you look at the screen through isn't at the edges - even on an "edge-to-edge" display, there's a tiny strip of opaque glass, so you can wipe the entire surface of the glass you look through without a problem.) But it's the carbide particles that scratch even Gorilla Glass 3, and replacing the glass (which is cheap, but takes a LOT of experience to do without damaging the rest of the phone - which means you pay labor for someone who's spent a lot of time learning how to do it right - read: not cheap) is a lot more expensive than replacing a $1.67 piece of plastic protector. And if it takes you 2 whole packs before you get it right (and I don't think anyone is that clumsy), you wasted $8.33, not the $10 for the glass or the labor to remove the scratched glass (that's the difficult and expensive part).
You could use tempered glass, but that's not hard, it's tough. IOW, it will scratch, but it won't break on impact as easily as gorilla glass. Some day they'll come out with cheap tough diamond sheet (anything crystalline is the opposite of tough) and we'll worry about breaking the plastic case the phone is in before we worry about breaking the screen. But after many years of doing this, and replacing screens that were protected by various means, I've come to the conclusion that the second best way of protecting the screen is a cheap plastic protector. The best way is an Otterbox case with a tempered glass sheet over the outside of the screen cover (and that takes about $50 for the Otterbox, $10 for the glass and whatever you pay to get the glass cut to size. I haven't seen any tempered glass protectors for the outside of Otterboxes.) If you're not in the habit of dropping your phone, a plastic screen protector is fine. If you are, or you have kids who might, an Otterbox Defender is great protection. (And I'm retired, so I don't make a nickel out of any choice you make.)