In the series one Noumu was able to completely heal himself after being frozen by Shoto Todoroki. All for One is in charge of the creation of the Noumus and he gives quirks to them. Then why doesnt he gives a regeneration quirk to himself and completely heals from the wounds he got from the battle with All Might?
It is just because he already had cicratized his injuries and because of that the Quirk had no effect!
From the wiki:
All For One once stole and tried to use this Quirk to heal himself from the heavy damage All Might caused to him, but because his body had already cicatrized those injuries, the Quirk had no effect and was considered useless.