"Finding the best team" is virtually impossible. Unless every team plays every other team, or unless championship contenders play each other in best of 5 or best of 7 series, you're never going to know who would have won more games if they had met more than once (see Nebraska vs. Washington via 2010).But Miami (OH) would not deserve a shot to be the champion more than Ohio State does. In reality, Ohio State probably has a good chance to advnace and maybe even win the whole thing. Miami is most likely going to slaughter. They may have nothing to complain about if they buy into that principle, but that's a principle that ignores the 'finding the best team' idea while trying to address it. Ohio State is a 1-loss team that doesn't make it. What if everyone else in the field all have at least 1 loss as well? Ohio State is punished because of the timing of their loss, then, and nothing more. 11-1 Oklahoma, which wins an easy Big 12 field but loses to OOC Florida, would get in. Maybe even win. Both OU and OSU would have lost to one good team all year. The difference is Oklahoma's came in a meaningless OOC game.
You do make a good point with the Missouri example, though, it would hurt CCGs. Teams should not get punished for playing in them. Even with a Final Four (I don't like 16 teams as this opens up a LOT of those scenarios) a similar scenario is probable to happens. I don't have an answer to that, right now.
But you were suggesting a playoff system without at-large bids, and solely only for conference winners? That can't happen. The independent schools, such as Notre Dame, would not have a shot. And it would not allow schools to be independent, something which is their right.
It's a matter of HOW you're going to decide your champion. Are you going to do it on the field, or in the polls?
As far as that scenario goes, Ohio State isn't punished for the timing of their loss, because the polls don't matter. They could have lost to Michigan in the last game of the year, and still have played for the conference championship and had a shot at the playoff berth. Their problem is that they lost the conference championship game, the most important game of their season, essentially the first round of the playoffs. They should be eliminated because they lost when it mattered most. That's how playoffs work, that's how championships are decided on the field - it's the only way.
As far as comparing Oklahoma and Ohio State - there's no point in doing that. They play in different conferences, they shouldn't be concerned with one another. If Ohio State can't win its own conference, it has no right to point at another conference and say "Well, that conference is easier, I could have won over there!" Just win your own conference - if you can't do that, chances are that you can't win the national championship anyways. I would go as far to say that if you can't win your own conference, you don't deserve a shot at the national championship (see 2001 Nebraska).
Somebody mentioned earlier that conference championships being used to determine playoff berths would actually be good for OOC play. Ohio State could lose to Florida without it hurting their championship hopes, which means that we could maybe have a few less Nebraska - South Dakota State type matchups through out college football's "preseason."
I also don't care about the independents. The NCAA could require them to join a conference, or they could simply host a play-in game between the two highest rated independents. There would be any number of easy, reasonable solutions to that problem which would allow the conference championship system to work. If you want championships decided on the field and not by the voters, it's the closest thing you're ever going to get.