The attention that the League was bringing to the Mob was more than just an annoyance.The FBI stepped up the heat,and all five Families were subject to constant pressure. Gambino had put the word out after the first Unity Day celebration that attendance at a second one would not be appreciated, and indeed the turnout was much less than expected. Despite some "friendly"advice from Gambino,Joe went ahead with the event.

Besides the negative attention,Colombo had been whacking up the donation money with the other bosses,and he was found in possession of a paper with Gambino's name on it along with a sum of money. Colombo's explanation was that it was "money that Carlo had raised selling tickets for the League"
This was a final straw for Carlo,and Joe's fate was sealed.
Although Gambino was at the peak of his power,I'm sure he went through the process,and made a formal case to the Commission for the hit.
Columbo's activities had gotten out of hand and would have put a major dent in the Mafia's earning power due to the Law Enforcement firestorm that would continue to be unleashed.

The Families would have nothing to gain and everything to lose by allowing the League to continue.