...a good start, but not a cure-all. I dare say there are more than four teams who are better than ND. Yes, they would've gotten in over a more deserving team anyway, but at least if it were a field of 8 or 16 they'd be taking the spot from a more deserving team who nonetheless probably didn't have a shot of winning it all.
I still favor 12 teams, obviously. Notre Dame would have gotten a first round bye-- which they earned by going unbeaten-- and then would have probably been beaten by either LSU or FSU, which ever won the 8 vs. 9 first round game.
It would have set up like so:
(1) Notre Dame
(8) LSU
(9) Florida State
(4) Oregon
(5) Kansas State
(12) Wisconsin
(2) Alabama
(7) Georgia
(10) N. Illinois
(3) Florida
(6) Stanford
(11) Louisville
The rough thing about this is the seeding. Since half of the bottom bracket teams (and 3 of the 4 highest seeds) are SEC schools, Alabama would potentially have to beat two SEC schools to get to the finals. There's not much to do about this, though, when the SEC has 4 of the 12 teams. If a committee seeds the teams it could swap Florida and Oregon to somewhat fix the problem.