I think the problem with your idea is that Magic Missile already does that. I mean I could see how you might do away with spell resistance and all but still that's not that great. It would still only be one point of damage. And the idea seems inherently flawed, I don't ever really know when the BBEG is at 1 hp, my DM doesn't divulge that type of information directly, sure I might get 'extremely wounded' but that could mean he's at 10 hp from a pool of 150 and thus 1 hit point per spell isn't really gonna help that much.

There is all of that and for your first two spells you have to touch them which is something that as a wizard (assuming this is who the spells are going to be for, if it's another class then you would want to specify that) I don't ever really like to get within face-beating distance.

I don't want to completely rain on your parade though, I like the idea if you want to scale magic missile by maybe implementing something like a 0th level and then higher version of it but you would have to be extremely careful, magic missile is already a pretty much universally useful spell.