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?

No, he knows that Satoshi Nakamoto, whoever they are, would not risk communicating with the world ever again. (its kinda obvious why)