HP, overall, has very little importance compared to the other six. A nature that improves attack will mean your hits land harder, a nature that improves defense means you'll be able to take hits better. Like, a Pokemon with high defense and relatively average HP compared to a Pokemon with low defense and high HP... you're gonna destroy it. Speed is also important too. HP can matter in terms of damage rolls but having a nature that improves it doesn't really seem to add to anything. Every Pokemon has a set in stone HP, and improving it by a small percent doesn't really make much difference to its overall damage-taking capabilities. I suppose it could influence competitive battling, but I think it'd make it more complicated.
But yeah... probably not. Although new natures might be possible in the games. Like natures that can influence two stats positively and two negatively at the same time, it'd add a new level of complexity to the games.
