Profaci was a perfidious bastard, pmac. In '57, Carlo Gambino, then Albert A's underboss, approached Profaci about whacking Albert. Profaci assigned the hit to the Gallos. Then, as you said, Frankie Shots was holding out on Profaci, so he assigned the hit to the Gallos again. He promised them some of Shots' action as a reward, but didn't give it to them. That started the war. Gambino began agitating for Profaci to step down, but he was supported by his pal, Joe Bonanno, and stayed on until he died in '62.

Then Joe Magliocco, his brother in law, became Don. But Gambino led the rest of the Commission in refusing to seat him, and openly encouraged treason against Magliocco in his family. Magliocco conspired with Bonanno to whack Gambino and Tommy Lucchese. But Joe Columbo, one of Magliocco's capos, ratted out the plot to Gambino. Magliocco was forced by the Commission to step down and pay a fine. They next went after Bonanno. But when he refused to step down, a war within his own family began. It was the beginning of a long, long decline for the Bonannos.