The "problem" with a playoff of more than 4 teams (maybe 8 teams absolute tops) is that (1) early games would be played on home fields (2) it would require dismantling or significantly restructuring the bowl picture and (3) it would almost certainly shorten the current 12 game + conference playoff scheduling model.
Playing on someones home field is a horrible disadvantage to the visitor especially if there is a considerable travel distance involved. And would an undefeated Toledo team get to host a game with a 3 loss BIG or SEC team? Probably not.
The bowl games are really "civic events" designed to bring money to the city without much regard to the actual quality and competitiveness of the game itself. IMO, there would be considerable resistance to something that substantially disrupts the current "conference partner" relationship.
I recognize that it will never happen but I have long believed the "best" playoff model would require a super division of 72 teams in 4 conference, each with 2 divisions of 9 teams. Only the 8 games (H and H) against your 8 division foes would count toward your divisional title. Schedule whoever and however you please with the other 4 games. The "first round" could be either a conference playoff or simply the start of an 8 team playoff. Any team not in the playoff picture would be eligible for bowl participation elsewhere.
Believe it or not, before the last couple of rounds of "conference realignment", it would have been possible to construct such a "mega-conference" structure with relatively little disruption to existing affiliations. It would have been done by dissolving the Big East and the BIG XII-II, merging those schools into the remaining 4 conferences and possibly relocating a few teams into a "new" conference.
Peace