Bear in mind that the tempered glass is no harder than Gorilla Glass 4 (actually, GG4 approaches synthetic sapphire in hardness). About the only difference is that when GG4 breaks, it breaks into large shards (which can stab through your hand), but when tempered glass breaks, it crumbles into tiny and not-very-sharp pieces. They both have about the same scratch resistance. (And it's pretty easy to get a cooling defect in glass, and have it shatter when you drop the phone - even if it's on the case, not the glass.)
Plastic, 3/$5 screen protectors aren't hard or tough - if you're careless you'll scratch them. But at $1.66, that's not too much of a concern (and my 4 year old one still has no scratches). AND - the plastic absorbs some of the shock, so the screen might survive a drop as well as a tempered glass protector. (And the pieces are held together if the protector is attached with adhesive).
Until we get transparent metal, that's about the best we can do. Hard, scratch-resistant protectors break, soft, shock-absorbing protectors scratch.