It is not the Big Ten's fault (nor the SEC, ACC, Pac 12) that they are able to attract and maintain more member-institutions to each conference. Why should the big xii be given special consideration here?
I do not recall the cry and hue of big xii fans during football season telling the world how advantageous it is to be able to play teams like Kansas, isu, Texas Tech (and recently West Virginia) every year. That is 30% (40% including WV) of not really challenging conference competition each season.
You began with a faulty premise - that being the big xii is obviously better 'top to bottom' without regard to why that might be. Now, it should be evident that the very bottom of the Big Ten is struggling more so than perhaps is usual (Minnesota, Illinois). That is the difference maker in your scenario. It should also be clear to now see that if the two conferences were to match teams using your preferred ranking system head to head that hypothetically the Big Ten would come out ahead based on those rankings. The averages of the best ten teams from each league indicates that.
The difference is that the big xii would not have enough teams to compete after a 10-10 match up between Nebraska and TCU. No one knows how good/bad any additional team from the big xii would be.
The Big 12 is better top to bottom because they only have 10 teams and the Big 10 has 14 plus the bottom teams in the Big 10 are much worse than the bottom teams in the Big 12. I don't understand in what situation the Big Ten would come out ahead in rankings considering taking away bottom teams from one conference and not the other doesn't work. You could say the top 10 of the Big 10 is better than the all ten in the Big 12 but top to bottom the Big 12 is better