Once the captains and part of administration found out conspirators had backing of other bosses they wisely remained on the sidelines, not risking themselves getting hit. Gallo probably fantasized himself getting the top spot but they grounded him ("You're no Paul").
In essence Castellano was the real deal and was feared as a boss, but not letting (except a handful of people, including Gaggi) anyone into his inner circle and squeezing everyone for money meant he had no hardcore backing of captains when shit was about to hit the fan. Gambino seems to have been more approachable and it's hard to imagine anyone pulling this act in his time.