I think that regional is best for all sports. Football only plays one game a week, so it can have several exceptions to the rule. The SEC has been the smartest — keeping as many games as possible within their conference footprint, including OCC games.
I'd be happy if they split football from the rest, created a legit governing body for it that makes, controls and enforces the rules equally, and evenly distributed accessibility (more of the NFL format). If college football is going to behave like a professional league, it needs some parity like the NFL as opposed to MLB (spend anything you want).
Basketball can be lumped in with the other sports.... or have its own NBA-like body.