This would create a very low-powered campaign in which everyone would be hell-bent not to fight and even the least powerful spell would kill instantly. Could this be any fun for you at all?
No, not for me or anyone I play with. At least, not as a D&D game, as someone else mentioned. Entire classes would become pointless. When all classes are equally deadly, those who specialize in dealing damage or combat applications weaken appreciably.
The notion that this would
reduce fighting is, IMHO, exactly the opposite of what would happen in a game world. Now, anyone willing to dare can topple them mightiest warrior, if they get the drop on him or are lucky. A child with a rock could defeat Smaug, potentially. In a world where everyone is fragile, the power will go to those who can be less fragile either by skill, magic or equipment.
Consider: what good are healers in a world where injury only falls into two categories: healed almost immediately or DEATH? Archers now become the mightiest warriors, able to kill from a distance, under cover (assuming mages never get past first level). The incentive to surrender or submit now becomes the last option: sheer numbers will win a battle, even if those number consist of hobbled old men with knives against minotaurs warriors. I mean, people haven't exactly stopped fighting in the real world, where lethality is still pretty high: this isn't going to change much in that regard.
I don't doubt that you could play a game like this and find a way to make it enjoyable. But even a show like Doctor Who features it's share of combat (side note: the old Dr. Who game from the 80s, iirc, did not feature a 1 h.p. system...it was more like FASA's Star Trek). But why would you bother doing this in D&D, then? Why not something like Dread?