"Best team" and conference winner aren't always the same thing and the former is subjective anyway. You could have a 4 loss conference champion that beats an undefeated team who happened to have one bad game at the worst time. Are they now a better team? No, they are the tournament winner which is what a champion really is with playoff based sports. The flawed concept here is trying to determine a best team.
It would be so much simpler to just have to play your way in via conference titles and if you are a one loss team that sits out because you couldn't get into and then win your conference tournament then too bad. An 11-5 Patriots team sat out of the playoffs one year. I'm pretty sure NC State back in 83 wasn't the best team but they sure as hell were the champions.
If you want playoffs then accept what comes with that as part of any tournament / playoff format. If you want a subjective best team award then go back to the pre BCS days, play independent bowl games and have writers tell us who the best it. I much prefer the on field approach and don't really care who the "best team" is.