For one thing . . . the Cotton Bowl ceased to be a major bowl once the Southwest Conference (whose champion received an automatic bid to the game) disbanded in 1996 and its top teams joined with the old Big 8 to form the Big 12 Conference. Those old days of SMU, Texas, Texas A&M, and Oklahoma never would have come back, regardless of what happened with Arkansas and the SEC.
The old "automatic bid" system penalized Big Ten and Pac-10 teams by forcing the conference champions to play against each other -- no matter how good or bad these teams were (I believe a 7-4 team that wasn't even ranked in the Top 25 could conceivably win an automatic Rose Bowl bid). Independent schools had a big advantage in seeking national titles because they could accept bids from any bowl game in which the #1 or #2 team was playing. This is why independents like Penn State, Miami and Notre Dame won a disproportionate number of the national titles in the 1980s and early 1990s under the "old" system.
My complaint about conference championships (or lack thereof) is not that they are necessary, but that comparing teams from conferences with these games to teams that don't have them is inherently unfair. In some of these cases (you brought up a good example with Nebraska) they serve only to force a good team with the opportunity to play (and possibly lose) one additional game -- and usually against a very strong opponent, too.
Conference championship games make more sense today than they did 15-20 years ago mainly because more and more conferences are now large enough that each team cannot play every other team in the conference during the course of a regular season. Heck -- the Big Ten has even refused to change its name even though it has had 11 teams for more than a decade!
Initially, the Big 10 & Pac 10 didn't care about the BCS and didn't participate. Eventually, the BCS money grew to such ridiculous levels that they caved and became part of the process. The Big 10/Pac 10 rivalry and the Rose Bowl mystique is still important to their member schools. Attendance at Rose Bowls where either confernce is not represented has always resulted in decreased attendance at the game.
I say they should restore the traditional 4 major bowl game affiliations for conference champs and go to a plus 2 playoff format.
And if that means a 4 loss team from the Big 10 or Pac 10 goes to the Rose Bowl, wins that bowl and beats two 1-loss teams in the plus 2 games - they are the national champs.