I agree that at pretty much any of those schools, it's not going to be ANYWHERE near as important as football.
But I think you're giving Texas short shrift here... Here's the Wiki summary:
When you start getting into the territory of ninth most NCAA tournament appearances of all time, I think you have to admit that although you're not seen as a traditional basketball power, it's likely more that your football program has overshadowed a basketball program that's quite good in its own right.
Indeed.
Maybe it's just because I'm a football nut and don't care in any way about basketball (unless Florida is winning another NC, lol), but it seems to me most fans don't have mental tiers when it comes to college basketball.
There's the blue-bloods (UNC, Duke, KU, UK, UCLA once upon a time), and newfangled UConn. Then there's.....who?
Indiana could be in the blue-blood group....I guess.
As a 45-year old, with no one obvious coming to mind, I go back to the old Big East I guess....Georgetown, Syracuse.....UNLV? lol
Purdue is definitely in there, but like looking around the country.....uhhh Arkansas? Washington schools, no, Oregon, no, Cal/Stanford no. USC, Arizona.....ah, Arizona is sort of a lesser UConn, timing-wise.
CU, BYU, Utah, OU, OKST, Texas schools.....for me, Texas doesn't stand out, but as the 9th-most tourneys, they should.
In my lifetime, I"m thinking 2nd-tier ACC schools have played more important games than much of the rest of the country. Virginia, Wake Forest.....Maryland for a time. None of the New England teams aside from Syracuse and St. John's seem to have mattered much. MSU is definitely in the next tier below the blue-bloods, thanks to Magic and Izzo. OSU does well sometimes.
Meh, I'm just rambling now.
Indiana, MSU, UConn, Arizona.....Florida?!? UConn really shows the all-or-nothing results that make this tricky. Are NITs a plus or a minus?
I just think it's hard.