Corleones killed the police captain only after Vito's two murder attempts the second one even as Vito lay helpless in his hospital bed

I doubt the hit on the top, most powerful, Numero Uno Mafia Don would have been carried out on just the say-so of Tattaglia a pimp Hence Barzini must have been on board, already picked sides

It is inconceivable one family would have monopoly, could never happen in real life!