Yes, money's what it's all about.
In another thread, I posted that, in the novel, only Tatt and Barz were whacked; presumably the other families fell in line under Michael, or at least stayed out of his way. Probaby FFC had Cuneo and Stracci whacked in the film to provide more drama for the ending.
BUT: The key is to look at what Michael wanted. He wanted to be "legitimate" in Nevada. But he also wanted to hold onto the NYC "olive oil business" under loyal Clemenza for two reasons. First, it was a continuing source of tribute, and made a natural synergy for Clemenza's high rollers to come to Nevada and be fleeced big-time at Michael's casinos. Second, Clemenza was Michael's muscle-in-reserve. Without the threat of his NYC army, Michael might have been a sitting duck for other Mafiosi wanting to muscle in on him in Nevada.
So, if Michael convinced the new heads of the other families that they had nothing to fear from him and Clemenza as long as they stuck to their businesses,kept peace and concentrated on making money, they'd probably go along with him. Money, money, money...
N.B.: In a deleted scene from II, Neri tells Michael that he's located Fabrizzio, who entered the US in 1956, "...sponsored by the Barzini family." That tells me that someone in the Barzini hierarchy thought it important to pay their debt to Fabrizzio. Although Fab was operating a pizza joint somewhere far from Nevada, and probably posed no threat to Michael, I'd still take that as a sign of lingering grudges in the Barzini family against Michael.
I agree completely even though clemenza was given control he was basically only street boss while mike was still the main man.