What about a 6-team playoff:
5 from the P5 Champions
1 from highest ranked
All six would be seeded with the top 2 teams getting a bye first round. The last four would play:
3 vs 6
4 vs 5
3-seed winner plays 2 seed
4-seed winner plays 1 seed.
This year, that would have removed the need for debate between OSU and LSU for the top seed, and allowed Oregon and one other team a chance...
One reason four works well is that even OU (yes I'm a fan) gets recruiting cred and pub along with the other three (even though I really don't think we belong). This makes those teams that are fortunate enough to be repeat participants selfish with sharing this advantage with other schools...
It's similar to schools like OU and Alabama wanting extra recruiting time/days for having to play in the conference championship game. Why would schools like Iowa State or Texas Tech want to give even more recruiting advantages to schools already enjoying the top spots in the conference...