Well, Alice does say something about "Da soul is made invincible, yada yada", but aplying that with no limits would kinda be a fallacy. I'm assuming Kaguya can no sell the soul attacks long enough to use her own hax because Wolf here is more or less in the same tier as her.
Just to make something clear: Kaguya has that lvl of Regen, but it isn't something absolutely instantaneous all the time. She usually fights until she can't stand the pain anymore. If she gets obliterated, she might reconstruct, but the pain stays and eventually it's too much to bear. Heavy injuries might last for a while... Not sure if the wikia is accurate on this one, but it says critical injuries might last days before healing.
Would be kinda strange to look at it like that, though. last time I played Imperishable Night, IIRC, Kaguya was getting obliterated and being restored mid fight.
Anyways, I did some research and the dialogue on the Hourai Elixir and its effects on the soul is as follows (this is for Mokou, but she has the exact same type of immortality that Kaguya has):
Alice: Do you think she's alive? She looks dead to me somehow... Or was she revived?
Mokou: How rude, treating me like some kind of ghost... But that's almost correct. Your ability to see through illusions is quite impressive.
"So, you ARE a zombie then?"
"Actually... Death is no longer a part of my existence. To be devoid of death is to be devoid of life. Free from the bounds of life and death... But I'm as human as they come. In a sense, though, I'm also like a ghost."
Alice proceeds to comment on how Mokou can't age nor die, and the conversation goes on. Mokou says she drank the Elixir and was made immortal, talks about how Kaguya tries to kill her and says how that is impossible.
"The Hourai Elixir is not to be consumed by humans... The forbidden medicine. With but a single touch, you will never become an adult. With a second touch, you will forget all disease and illness. With a third touch.... Your soul will forever churn in torment!"
*Fight (and a ton of shots) ensues... Mokou gets defeated and the more talk about the immortality.*
Marisa: "Shall we do it again? Maybe you really are invincible." Alice: "Invincible, maybe, but she seems worn out." Mokou: "I've already reached my limit. I'd better stop before I'm unable to move tomorrow."
Alice: "Don't waste time wondering about something like that (on the topic of cutting Mokou in half to see which side would remain). Immortality is like casting away the physical body. Only the soul becomes invincible, it's constantly reborn in new flesh. Souls don't have a particular size, so they can freely create another body. By contrast, I guess that any body without a soul perishes rather quickly...?"
Mokou: "As I am undying, ghosts are unliving. Maybe it's only a little difference in form... or guts."