By this, I mean those conference officers and bureaucrats who would control the day-to-day stuff, and who would be personally involved in negotiations with networks, sponsors, venues, etc.
Compared to independence, more is taken care of for university administrators (who seem to enjoy their other duties, anyway); much of the sports stuff is farmed out off-campus.
For higher-ups at conference H.Q., representing dozens of schools gives them more leverage in their contracts with broadcasters. The ability to split off from the N.C.A.A. completely has also been mentioned here.
Having oodles of guaranteed inventory gives broadcasters more leverage with cable distributors, whom they'll press for higher carriage fees.
Sure, there's a limit to how far this can go, but for the individuals who are driving this, there's increased control and status on the line.