I'd say that picking what kind of power goes against the story of MHA. Most people are born with completely trash powers. Statistically speaking, we'd all end up with mutations that would ostracize us from society while providing minimal ability to actually be of any use in any situation.
Physical wounds especially heal with time. It may sound hard to believe but humans do in fact have healing factors. I suppose time won't heal a severed limb, but that's what prosthetics are for.