They are the ones who have all the power, not the commissioners, not the ADs and certainly no one outside of academia. They have been open and vocal about the opposition to expand if it meant adding another week or two to the season.
The SEC broached the idea of an expanded playoff, at its spring meeting, and the ADs and coaches were in favor of returning to an 11-game schedule to accommodate an 8-team playoff. Saban wanted to keep the 12-game schedule but do away with the CCG.
An 11-game schedule would be anathema to all schools who have no chance to even sniff a NY6 appearance because it would mean, at the very least, that on alternating years they would lose one home game. It also means that would would lose one money game, against a P5 every year. I see all those schools as voting against expansion.