This isn't college basketball. If you're going to allow non-champs into the CFP, just remove the Conference Championship Game and make up for it with all the money that will be made by expanding the CFP.

You could also remove the divisions too, so conferences aren't hampered by divisional and cross-divisional scheduling, unless they want to be. You could still have certain in-conference scheduling groups or annual rivals. This would benefit the 14-team conferences greatly, so that certain conference members play each other more frequently.