I'd put it a little differently. Michael wanted to think of himself, and be thought of, as "legitimate"--but on his terms, his definition. The scene in GF where he woos Kay in New Hampshire says it all: "My father is no different than other powerful men with responsibility for others..."Senators and Presidents don't have men killed." "Now who's being naive, Kay?" Or, in 3: "Just when I thought I was out, they pull me back in." Was he ever out? Even while Abbandando was BS-ing the press about Michael selling the casinos, "the Pope this day blessed Michael Corleone," Vincent is telling him how everyone knows he's like the Pope, is preventing Zasa from rising in the Commission, etc.