Genovese was as heavy as you could get. Simply put, guys were afraid of him. The bosses who weren't big on him (Costello, Anastasia) were muscled out and the remainder (Lucchese, Bonanno, Profaci) didn't necessarily care what Vito did as long as he stayed out of their respective families. Lansky, despite what some say to the contrary, was finished as a shot-caller now that Lucky and friends were out of the picture. Gambino owed his spot to Vito (if you follow that line of thinking) so he backed him for the initial period of his reign.