@DarknobleOtaku with only regeneration immortality... Yep... For example the head thing you told me about, izuku would have to wait to regenerate his full body. And he feels the regeneration.
Meanwhile with being indestructible or to put it in another way to understand better (becoming unbreakable)... He won't ever get injured because someone indestructible won't ever get cut, slashed, pierced... Or have any harm in his body. He still feels the pain the attack could do if he wasn't indestructible, but only for a few maybe potentially a split second.
So if you combine the two. Izuku can't get injured, he won't age, but still feels pain for split moments. He won't have to regenerate because his body would be unbreakable. But like I said it would be boring and less fun to write.