I don't think that is the correct analysis on Duke. If you take Duke, you are not taking them for any of the reason you have taken anyone else into the Ten. Not football. Not football fanbase. Not football market. And, while it's a great school, the Ten doesn't need a small private school for its academic image.
If the Ten takes Duke, it is because they are being brought in (i) because you can't get UNC otherwise and UNC is worth it, and/or (ii) because Duke is the #1 basketball brand name and in your national ouperconference you are willing to tie up one spot for your hoops.