One way of thinking of it is (i) money (yes, I know you mentioned it, but there's a lot; more below); and (ii) if you are Oregon or UW and really want to win a natty, you're going to have to be good enough to beat almost all of the other good teams in the Big Ten. You don't even need to be the conference champ, necessarily. That wouldn't be that hard ... look at the current Big Ten West. Increased access to the playoff will help the remaining Pac-12 schools, since Pac-12 schools will be able to say you can win a natty in the Pac-12, but a lot of other things are going to cut in favor of the Big Ten and SEC in recruiting based on $, exposure, and the perception that those two are the superconferences everyone else clearly is behind. If the money picture is as disparate between conferences as I think it will be, you probably will have a lot of years where the Pac-12 champ gets in and is bounced in the first round or by a top 4 team in the second.
As far as money goes, a lot of this is speculative, but if Big Ten schools get, say, $85m a year just from the media deal, with the Pac-12 schools getting $35m, you're up $50m every single year just from that. That's without even counting the likelihood of greater CFP/bowl payouts just from being in the conference, with those being significant. You get more with 1/16 of 2 teams' shares than 1/12 of one team's share. This isn't "just" the Big Ten schools getting 33% more or something like that, like getting $30m instead of $40m. It's almost 3 times as much, just from media rights.