As Apple said: as long as Vito breathed, Sonny was not only not going to make a deal, but would continue the war. Plus, Sonny was too dangerous to the other families to let live. By killing Sonny, Barzini/Tattaglia seriously weakened Vito's hand and hastened his compromise. And FFC no doubt had been mightily impressed with the "death by machine gun" ending of Arthur Penn's "Bonnie and Clyde," and wanted his own version in GF.