I think that pods are the compromise here.
LIke you, I think it is best to have a group of teams that you play annually because that feeds rivalry.
OTOH, I think it would be ridiculous if Ohio State becomes conference-mates with USC and UCLA and plays them LESS frequently than back when they were in a different league.
Pods split the difference by giving each team a group of annual games and still playing all league teams once in a while.
I don't think you need strict, formal pods to do this. That's why I like the idea of each team having 3 (or 4, for Fearless) set, annual games, but they don't have to be the same set teams as others in a specific group. Then rotate the rest of the schedule as you like, without the formality and limitations of ensuring pod boundaries are maintained. It accomplishes the same goal, but allows more flexibility.
If I set up the following pod: Ohio State, Michigan, Michigan State, and Minnesota, those teams are forced to use up some of their annual slots against teams that might or might not be that important to them.
But if I just say, every year Michigan plays Ohio State, Michigan State, and Minnesota, but Ohio State gets to play Michigan, Penn State, and Wisconsin, and every year Wisconsin gets to play Ohio State, Minnesota, and Nebraska, it's a lot more flexible. (yeah I made up the perma-rivals, they probably don't make complete sense, forgive me I'm not a B1Ger...

).
Additionally, I really do like FF's suggestion of simply admitting you don't need to schedule every team in the conference. Why should Nebraska ever play Rutgers? Let's admit it's an undesirable game, admit that in a 16-team or 20-team conference, the idea of playing everyone is silly and antiquated, and just try to schedule some fun games!