By the time of GF3 Vincent is the only relative that is capable of continuing the Corleone family IMO. He may not be as patient as Michael but there are no others who would be up to the task.

He has a lot of Vito's qualities - he cares about the people of his neighbourhood and is loyal and protective of those he cares for. He does have Sonny's temper but he also has absolute respect for Michael and wants to do his part for the family. He refers to Michael as the 'saviour of the family' and you get the impression he wants the security of the family to be ensured.

I'm in two minds about GF4, I love the trilogy and would like to know about what happens afterwards but I'm also someone who believes the whole GF saga is about Michael Corleone.