Of course TB, it's not unusual for some of us to mix the novel with film. So, I'll do it.

In the novel, Sonny's murder was not intended to win the war for the Five Families; it was intended to stave off their defeat. As the novel also states and as Tom told Sonny, business is starting to open up after the newspapers linked McClusky with the rackets. So, even with Sonny gone, the Five Families would have seen the virtue of letting things continue to calm down. Remember, the Families prepared for the bloody war of revenge that they were sure Vito would unleash on them for Sonny's murder. So, while Sonny's generalship was greatly valued, the Families knew that Vito's generalship was even more valued and they still needed him. Vito was still in the catbird seat.