the major football programs would simply coalesce into their own league and leave the rest of the conference sports and conferences themselves alone as they are. The wear and tear on every other sport, who largely compete more often than football and tow along family and fans, would be significant and bring real harm to that whole landscape. Geography obviously played a big part in how these associations formed. For the college experience it ultimately is, this is getting lost.
Put your top football dogs together, form divisions, sport your league logo in games and standings, schedule accordingly, and divvy up the mega proceeds. I don't necessarily think it has to envelop all of the rest of what these conferences are and how they serve the students, including basketball. Basketball gets a huge tournament at the end of the year so it really doesn't factor too much on the conference end. Lots of games also with plenty of good OOC opportunities.
Maybe develop a system where there's a top 32 then the rest and have a promotion / relegation mechanism in place? 8 games versus the top tier and 2 or 3 against the rest? Ensure rivals meet, whatev.