There are lots of programs that were "powers" at one time, but when they got passed by by major conferences, they pretty quickly fell off the map. Exhibit A is new AAC member Houston. While they didn't win a title, they were a major program from the 1960s through the 1980s. Final Fours in 1967, 68, 82,83 and 84. Lost in the finals twice if I recall by NC State in a huge upset and by Georgetown in its only title. Turned out a list of stars. The 1968 team with Elvin Hayes upset the #1 UCLA Bruins with Kareem in what was the first "Game of the Century". And remember in the 1960s and 1970s, getting to the NCAA Tournament was MUCH more difficult than it is today. No such thing as at-large bids in the same sense we know them today.
Or take Holy Cross. While they weren't on that level, they were certainly on the same level as UConn and probably the 2nd best team in New England at the time of the Big East. Won an NCAA title. Won an NIT when that was considered equal in the 1950s. They elected to pass on the Big East when offered and were replaced by UConn. Now they barely register. I know you don't want to believe it, but in college basketball your conference very quickly becomes you destiny. It happens in lots of little ways. Seeding, for example. Mid-majors rarely get a top 4 seed and suddenly your road becomes much tougher. With 14 out of 18 garbage games in conference your RPI suffers and you can't make it up with non-conference games, instead of getting a top 10 ranking you find yourself topping out in the top 15 or 20. It won't be over night but it will be a slow and steady erosion of status. We very likely will end up as one of those top mid-majors, along with the Butlers and Memphises, and Gonzagas. But how many championships do they have now?