As I remember, there were marks, that were given to both of them, which disappeared after they sealed Kaguya. While some say that the marks awakened their abilities, but they might also be explained in another way.
There is no indication that I remember, that Asura got a mark when he got the SOSP power mode, therefore the marks could only be the sealing jutsu. So they both got power upgrade and sealing jutsu powered by the SOSP. Then even after they used it, Naruto still had the same abilities as before, same cloak, he could still levitate, he could levitate all 6 clones of Kurama and still had 3 more orbs (wonder why he didn't make more, they seem to be using them up). On top of all that, he didn't really seem to gather any/much natural energy, until he made those 2 crazy Rasenshuriken.
To be precise, he never really displayed the need for healing like Obito, Madara, and Kaguya did, because he didn't get hurt, until the end fight. He did seem to display slight decrease in power/compensated by alternative power and skill in the following 2 movies, e.g. super punch, ability to separate from Kurama, a beast size Rasengan, still levitating on the moon, healing quite fast from a sword wound in a minute or so in the manga.
So all in all, it is the extreme level of healing and the truth seeking orbs that are really missing later, maybe as existing answers pointed out by not having all the bijuus like Obito, Kaguya and Madara, actually that is when they were making them. Although Obito made a staff even after being exhausted to deflect Madaras orbs.
But then Naruto get Kurama times 2, so I think that is compensated. Still, he should have been able to make orbs after that. Regarding the arm, maybe he didn't have the energy to heal it at the time since Kurama went to sleep, although even later as an Uzumaki he should still display some amazing healing ability like Karin and his mother.