Not one of the other New York Families were ever going to let it happen.
The Genoveses were being run by Funzi and Benny Squint, The Lucheses, who were Carlo's biggest allies when Tommy Brown was alive, due to family alliances, were being led by Carmine Tramunti, while Tony Ducks was in prison, and had strong links with the Genoveses. The Columbos had Persico as Boss, and he would never kowtow to Gambino and the Bonnanos had Evola and later Rastelli. Rastelli was a weak Boss, and while he may have not had the strength to stand against Gambino himself, other members of that Family would never have let it be taken over.
Carlo probably had the biggest influence of the Commission members in the time under discussion, but I think his actual power had lessened since Tommy Luchese died. I also believe the Genoveses were probably the strongest Family again by that point; assuming they were ever not.
I agree completely, I think that people confuse the most powerful family with the boss who had the most influence on the Commission. There was never any evidence to indicate that the Genovese stopped being the most powerful family in NYC, if not the entire country. As for Gambino's plan, it probably would have failed miserably. He and Luchese had a hard enough time getting Bonanno to step aside, the Gambinos trying to impose their will on the other four families would have ended up in a blood bath, with the body count highest on the Gambino side. Also, if I remember correctly, by that time he had already had Castellano stand in for him as acting boss a couple of times because his health was failing. I doubt that he would have been well enough to engage in what would have been a huge war. Castellano would have had to have done a lot of the heavy lifting, and from what we know about him I doubt that he would have had the stomach for that type of thing.
