What is a national champion? There have been 96 teams voted #1 or who won a BCS or CFP since the writer's poll began in 1936. Of them, 92 have won all their games or all their games but one. Two of the other four had a loss and a tie. In modern college football, the ties would have been resolved into wins or losses and the teams with two losses would be out of consideration. The other two are the 1960 Minnesota team that had one loss and then lost their bowl game and would not have been considered for #1 in a post bowl poll, (which didn't start until 1968 for the writers and 1974 for the coaches), and the 2007 LSU teams. In 2007, everybody lost and everybody but Ohio State and Kansas lost twice. Kansas came out of the blue and was only ranked 8th in the BCS standings. LSU was ranked the best of the two loss teams and they beat Ohio State in the BCS title game.
Conclusion: a national champion should be a team that won all it's games or all but one. But teams that aren't at what we would not call a power conference level don't get serious consideration because it's presumed that if they played a power conference schedule they would not have such a record. A Boise State might have a bowl game against Oklahoma you could make a movie of but if they were actually in the Big 12, (of that time), they would not have been undefeated and probably have at least two losses. Thus, a national champion should have played a power conference level schedule and won all their games or all but one. Any such team should be in a comprehensive national championship tournament. If any are excluded the tournament is not comprehensive and not valid.
Because of that the 2 team tournament the BCS was rarely valid and the 4 team tournament the CFP will usually be valid but, as we have discovered this year, not always. We need a format that will always include power conference teams with not more than one loss.
I also feel we need a format that gives the Group of Five teams a path to the playoff. The whole reason for having divisions is to give everyone a shot at a championship. Every team should be able to win one if they just keep being the team in front of them until there's no one left to beat. If that's not possible, either they belong in another division or the playoff format need to include them. The Group of Five consists of teams who have migrated from FCS, (formerly Division 1AA), including several former champs. They should still be there, giving the Dakota teams some serious competition. But moving teams down seems to be impossible so the 1A, (FBS) playoff system needs to include them.
Eight teams, (I think that every team should have to win the same number of games to win the title, so I'm against byes), with auto bids to the power conference champions and another to the highest ranked Group of Five team would be a substantial improvement and might be enough to end any controversies. The powers that be want 12 to increase the number of power conference teams so they can get more money. The best idea for a tournament would be 16 teams with auto bids to the champions of all 10 FBS conferences and 6 wild cards. And that's perfectly doable. FCS has a 24 team tournament. DII has 28 teams and DIII has 32 teams. Have the Sweet 16 in early December, the quarter finals on new Years Day, they semis a week later and the College Super Bowl the week after that. You could still have the other bowls, if anyone wants to play in them.