I've never bought into Michael's seeking legitimacy (as most people define it) or that society in New York or Nevada would have granted him any legitimacy. How could the people in those locations not know who he was?

In prior posts, I, TB, and others have extensively commented on how Vito and Michael defined legitimacy concluding that it was quite different from the way most people define it. Regardless, a high profile Mafioso is not going to be legitimized.