The timing of Vito's death was convenient to the script. But, I'm guessing that Barzini would have continued to wait until Vito died to move against Michael. I think he underestimated Michael, and believed that Vito was still in charge--the power behind the throne--and he didn't underestimate Vito. He may also have been mindful of Vito's threat at the Commission meeting that if anything happened to Michael, "that, I could never forgive." (Yes, that threat applied to interference with Michael's return to America, but Barzini might have feared Vito's revenge for any lethal move against Michael). I also infer that Barzini didn't have to rush to kill Michael because he seemed to be doing just fine, chipping away at Corleone territories just short of provoking retaliation. In his mind, he could afford to wait until Vito died, and "weak" Michael was deprived of Vito's council.