If the other conferences were smart and NOT short-sighted (and we know this to be untrue), all non-SEC/Big Ten conferences would cozy up to the punching bag that is the NCAA and present a unified front to the SEC/Big Ten. Basically, tell them to eff off with their football demands and let them know that if/when they choose to break away for football, they'll be unwelcome to participate in any other NCAA sports (including the men's b-ball tourney cash cow).
People just do not understand the level of infrastructure necessary to provide administration/structure to dozens of sports. It's easy to crap all over the NCAA - and, rightly so in many cases - but what they do isn't easy. The SEC league office probably has about 30ish employees. The NCAA has more than 3,000.
Telling those two leagues to administer/govern 30+ sports would stop them in their tracks because no conference has the infrastructure in place to do it and it'd take many, many years and tens of millions of dollars to get to that point.