Except that no one wants to play a title game where weather can have a major impact (although the NFL is about to try it in the Meadowlands for what I suspect will be the last time as a reward to the state for prostituting itself to build it). Pretty consistent throughout the sport. I'm assuming of course that you would give all revenue from playoff games to the conference whether neutral site or home. With that assumption yes the schools will get more money. They'll also have to take over all the promotional expense and local sponsorship (and have to figure out how to get alcohol sales involved in concessions). There would be a not insignificant administrative burden taken on. Schools would probably still get more money overall but it would depend. Big 10 sets a lot in store by the history of the Rose Bowl. Too much departure from tradition takes College further and further down the path of just being the inferior pro-league. The major bowls have very valuable brands. That's something you can't reproduce.
The Big 10 btw obviously has better off alumni and you know it.
Sure the alumni are better off but a significant portion of the fan base is not alumni. Michigan and Ohio State wouldn't fill their 100k stadiums if the only fans were alumni.
As for weather at a neutral site that's an easy problem to fix. Just have the game at Lucas Oil or Ford Field (Lucas Oil is probably the best). I believe Indianapolis just proved with this year's Super Bowl that it can be a fine host site; the city is basically built for hosting major sporting events.
As for a non-neutral site I don't have a problem with weather being a factor. The NFL does it and with great success. I think championship games should always be at a neutral site, go ahead and put it in Pasadena or New Orleans or wherever, but I don't see a major issue with the #1 team getting a little weather advantage over the #4 team.