I'd love a system that included more teams + still kept the regular season valuable. What I support is:
-- 10 teams are eligible for post-season consideration (can't have a 10-team playoff!!!)
-- 6 teams get a bye; the other 4 play each other, at the site of the better seed
Advantage: Being in the top six means you get a week off before the playoffs and don't have to have a play-in game
-- With 8 teams left, the highest four seeds host the lowest four seeds
Advantage: If you're in the top 2, you play a team that just had to play the week before. If you're in the top 4, you get a home game
Now with 4 teams left, you have them play at the neutral sites.
This gets us 10 teams in the discussion, but there are huge benefits to being top 2 (bye, HFA, play a tired team), top 4 (bye, HFA), top 6 (bye) and top 8 (HFA in round 1). Literally every step of the way there are small benefits, so that team #1 has a significant edge over team #10. But at least every team has a *chance*.
I'd do autobids to the conference champs but still only if they're in the top 14 or 16. An 8-4 Big East champ is still SOL, IMO. But that's not a huge detail and one I'd give in on. Otherwise, last year we would have had:
1 - LSU
2 - Oklahoma State (IMO, committee would have seeded them ahead of Alabama)
3 - Alabama
4 - Oregon (think committee would seed them above Stanford)
5 - Stanford
6 - Arkansas
Then you'd have Wisconsin, Boise State, Clemson and one other team. Maybe Kansas State, maybe South Carolina, maybe Michigan. This gives us some buffer -- Houston would obviously be there had they won and that's key. There won't always be 10 deserving teams, but there will almost never be 11 deserving ones.
So in round 1 we might have Boise State @ Clemson and Kansas State @ Wisconsin. The winners of those two games would have a much more impressive body of work, and at that point, are reasonably eligible for an 8-team playoff.
How fun would this have been?
Boise State in Baton Rouge
Wisconsin in Stillwater
You could have the committee elect to avoid rematches if you want, and have Arkansas play Oregon and Stanford travel to Alabama. Those games would be incredible.
Then put the winners of those games in two bowls. At that point, you have a real national champion. One who has earned it.