I just want to point out the one "common" case in which allowing negative hp would be beneficial, since I don't believe anybody's mentioned it:
I've set up an elemental damage system where I encode the damage in the ones digit of the decimal damage number, and the actual damage in the higher digits. Then, every frame, you compare Link's hp to his hp in the previous frame. If he took damage, you can tell exactly what element it was, and adjust his hp to the correct amount based on weaknesses, etc.
The problem hits when your hp gets too low to take the full damage from an attack. To get around this I add around 1000 hp to link to make sure it never goes negative - but this messes up the built-in hp meter, and the save file, and a whole bunch of other things, meaning you need custom scripts to handle all of them.
Of course, my specific case is a bit complicated. But I've seen several other people (attempt to) use the "compare hp to last frame and then do something" strategy, that disallowing negative hp makes difficult. Ideally, the game would allow hp to go negative, but all the built-in aspects like the health meter and such would treat it as 0.
I understand if y'all don't want to do that, though.
