There's the difference between Vito and Michael. Vito, who saw his father, brother and mother killed with impunity by a more powerful man, wanted power to keep himself secure, and to be strong enough not to be "a puppet on a string pulled by the pezzanovanti." His idea of legitimacy was to run his world as he saw fit, and to dispense "justice" and "order" to his suppliants. He never deluded himself by thinking he could be considered "legitimate" like the politicians he controlled--he simply used them toward his own ends. He aspired for Michael to be "legitimate" by becoming one of them--a senator or governor.
Michael never understood that he could never achieve real legitimacy as a crime boss while posing as a respectable businessman. He never saw that the "legitimate" people he associated with would never consider him one of them because their "legitimacy" would be tarnished by his overt criminality. He was clever, resourceful, at times brilliant, in pursuing his goal. But he never got it--he constantly won battles and lost wars because he never understood that he couldn't be a top Mafia boss and a "legitimate" businessman at the same time. That's the real tragedy in Michael's life.
But the whole "going legitimate" plan was one that Michael and Vito cooked up. It wasn't just Michael coming up with plans after Vito's death, the last conversation they have before Vito dies is about planning for how things are going to go down after Vito's death.
At the end of the conversation Vito does express some regret at dragging Michael into the business, but then I'm mindful of the birthday party scene in Part II, where Michael announces he's joined the army, and where Tom tells Michael that Vito and Tom have been talking about Michael's future. I think it's pretty clear that Vito's original plan, before Michael joined the Army and the whole Sollozzo mess and Sonny's assassination, was for Michael to take a legitimate course that would end up with him in a high political office (Senator Corleone... Governor Corleone), but as Vito himself says "There wasn't enough time".
I imagine Vito's original plan was for Sonny and Tom to run the "business", while Michael would split off and become the legitimate side of the Corleones (with a lot of quiet support from Vito and his political and union contacts).
It's largely what Michael was trying to do by Part 3; where Mary is essentially in the same position he was as a young man, destined to legitimize the Corleones, while Vincent, like his father before him, was supposed to take charge of the business.
