Logic is on your side, Toad. But, it doesn't take into account Michael's overarching lust for power, and that his power is rooted in criminality. Even as he's celebrating being made a Knight of St. Sebastian, and inviting the press to his party, Vincent reminds him that he's still "the Pope" of the underworld. Even as he claims to have "sold the interests in the casinos," he's presiding over a Commission meeting--fellow big-time criminals. And, in Sicily, he's ordering an updated version of the Great Massacre of 1955.
In the novel, Vito said more than once, "A man has but one destiny." Michael's destiny was to be a criminal. Yes, he certainly sought "legitimacy," but on his terms. The most revealing statement is in GF, when he's wooing Kay in New Hampshire. "My father is just like any other powerful man with responsibilities toward others," he says, "like governors and senators." Kay remonstrates: "But governors and senators don't have people killed." "Now who's being naïve, Kay," he replies. Sure: if they can be considered legitimate, why can't I?
I don't know. I still think Michael's quest for power was all aboutlegitimizing the family. But the theme of the films seems to be that getting a Mafia family out of organized crime is well-nigh impossible. You need to be able to cower your opponents in the underworld with naked demonstrations of force; the killing of the heads of the Five Families at the end of I, the second set of executions of Michael's enemies in II, and the third set of executions in III, though that was technically done by Vincent, as the Immobliere deal had at least technically washed Michael and the legitimate side of the family of their sins.
Michael wanted sufficient power and wealth to basically buy him security and legitimacy, and to make sure that the other Families or any other criminal interest would never come after the Corleones again, and with the death of Altobello, the Arch-bishop and the others who had conspired to screw him over on the Immobliere deal, he came pretty close.
