TB, Michael's desired legitimacy would be much more than tarnished by his criminality. Who didn't know he was a criminal, a Mafia don at that? I don't see how he could ever entertain the fantasy of achieving legitimacy. Joe Colombo tried it a version of it, but who was buying it really?
But, of course, we've opined on this Board about Michael's (and Vito's) concept of legitimacy and how it differed from what most of us conceive of as legitimacy.