Wichita or Wichita State, they've been known as both, has not had a football team in 30 years, and hasn't had a relevant football team ever. They always bordered on something between lousiness and medicrity, until the plane crash in 1970 that decimated their program. They hung on another 16 years, but went away.
I remember when they were a part of the old Missouri Valley Conference that included Tulsa, North Texas State, Cincinnati and a revolving roster of teams most of which didn't play football. Drake, Bradley and St Louis were hoops teams, but not football.
OSU was a long part as then Ok A&M. They left. Memphis came in briefly, then left. Louisville came in briefly, then left. The conference has lasted in basketball. But those wanting to be a D1 football program at the bottom end of that, found new friends to hang out with.
Now, several of those programs are among those the Big XII is apparently considering. But not Wichita.