I wouldn't but others might for the "feel" reason posted above (even though I select films based on how close they feel to glass).
How do they protect the screen better? In what situations would glass protect better than a film?
Glass screen protectors have a silicone layer as the adhesive instead of the static cling type adhesive. This helps with shock absorbance, however negligible it may be. Also, when the glass screen protector shatters, it does not penetrate the silicone later. The glass layer also takes most of the hit from an impact, so a broken iPhone screen is much less likely.
A film would not protect against an impact to the screen as it is thin and flimsy. The simplest example of this, even though it may be exaggerated, is the video where an iPhone with a glass screen protector is struck by a hammer and doesn't shatter unless repeated hits are made with force that probably couldn't be replicated by a simple drop.
As for the video I reference, I don't have it on hand. It was some Swedish glass screen protector, but if you ask me, all glass screen protectors are tempered similarly.