Herm, that is an interesting take on NCs, although I can't say I agree.
My POV has always been that since college football doesn't have a playoff tournament, the season itself is the tournament- and it's single-elimination.
How do you feel about seasons with no undefeated teams
There is no real National Champion for those years. Take 1983: Miami is considered the MNC for that season by virtue of beating Nebraska in the Orange Bowl, but they got that game at home- an advantage no other bowl participant had- and they got killed by Florida in their opener, 28-3. Can you
really give a MNC to a team that got lost a game by 25 points? Does Miami
really have a stronger claim than, say, Auburn, which had the same record, played a tougher schedule and didn't get a home bowl game?
or seasons with multiple undefeated teams?
I think any team that goes undefeated has a right to claim the National Championship. If Auburn and Utah in '04 or Boise in '06 or Utah in 08 claim the NC for those seasons, I have no argument with that. You can point out deficiencies in those teams' schedules- including 2004 Auburn, which played a horrible OOC schedule- but the bottom line is they did everything they needed to do in those seasons. BTW, the '94 Nittanys have a legitimate claim to the MNC for that season as well, although Nebraska did have to win a road game against Miami to clinch their undefeated season.
In my mind the "purest" National Champion is the team that goes undefeated and beats another undefeated team in their bowl game. 2002 Ohio State and 2005 Texas are the closest thing to pure National Champions we've seen in the last two decades.