So, let's talk about Craig Wright a bit more
My argument:
Craig Wright's claim to be Satoshi Nakamoto is ultimately false as he does not support axiom of resistance and is not a bitcoiner, no matter he has or has not access to Satoshi's private keys. His probable access to the keys could be used as an evidence for conspiracy accusations against him in courts.
My answer would be, whether Craig Wright supports the axiom or not is irrelevant. If I express my support for the axiom would that make me Satoshi? How can I be if I don't have the keys to prove I am him?
Holding a key just proves one thing: you have rights to spend a balance, not holding it means you can't do it. Your identity has nothing to do with your possession of keys, it is a social issue and should be addressed socially.
It is why I think Wright's social behavior leaves no space for him to steal Satoshi icon, he is not a bitcoiner as I discussed above, being Satoshi himself? Noways!
But if Craig Wright held the keys, and used it to verify that he is Satoshi, it would not make the community think more him, but it would unquestionably make Satoshi look less.
Bitcoin will not care.