Just an idea. If Craig Wright is NOT Satoshi Nakamoto, he would definitely risk the real Satoshi come up with a proof, that Craig is not SN. Is it possible, that CW explicitly knows about the death of the person behind SN, so he can make his claims without backing them up with a proof?

That's possible because there's a possibility that the real Nakamoto could come out and that will embarrass Craig Wright, I guess he knows the real cannot come out anymore, unless he gives out a will to his inheritors and that includes the private key,he is exploiting something that he knows.