Let me see about Tulane...
AAU member = good.
Other members in the Big 12 include Iowa State, Kansas, and Texas. Hence, Tulane would actually be, academically, better than most of the rest of the conference.
Association of American Universities - Wikipedia, the free encyclopedia
Total enrollment = about 12,500
That would be the smallest in the conference, as Baylor is about 15,000 or so. This includes Louisville as the eleventh member before then near 15,000 as well.
Academic endowment = $888.5 million
They have a medical school, so they're kind of cheating on that one, but Iowa State's is about $500 million, so they have us beat on that one.
Football by the Sagarin rankings:
Tulane (174, 135, 141, 148)
ISU (34, 65, 66, 114)
KU (90, 119, 62, 31)
Yeah... they're going to need some work in that department...
MBB:
According to Sagarin, Tulane was 94 in basketball last year. That was better than Texas Tech and Texas A&M in the Big 12. That was also better than TCU, though I do want to say that Louisville and West Virginia both have very strong basketball programs on the whole.
I think, actually, I'm on the side of the OP here. They look like a good addition. They also expand the footprint of the media markets. I think it would require some sort of understanding between the rest of the conference and Tulane itself on putting a much greater emphasis on athletics--particularly on football--than what they have had it in the past, but I think they seem a peer institution with a lot of potential to compete. I would certainly welcome something like...
Big 12 North
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Iowa State
Kansas
Kansas State
Louisville
Oklahoma
West Virginia
Big 12 South
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Baylor
Oklahoma State
TCU
Texas
Texas Tech
Tulane