Because (1) it would have a TV deal that is perhaps 10% of the TV deal the 2-sport conferences have (2) it would be a league that might - might - get 2 NCAA bids early on (3) four years from now it would be a 1-bid conference (4) 10 years from now it would be defunct for all intents and purposes since the two-sport schools won't be in the NCAA anymore. It's true that you might be able to dominate the NCAA tournament, if you're happy beating ODU, Richmond, Cleveland State, etc.. Just don't expect to be playing UNC, Duke, UCLA, Syracuse, Pitt, Kentucky, Lousiville, Michigan State, Indiana... you get the point.
There is no room for basketball-only conferences on the national stage. 10 years from now basketball-only schools will be basically MAAC or NEC level programs.
It continues to amaze me how overrated the "Catholic League" basketball programs are by our posters. Providence, Seton Hall, SJU, DePaul have been awful for a decade or more. The 80s were a long time ago. Marquette is a nice program. So are Georgetown, Villanova, and Notre Dame. But here's some context for you: the "Catholic League" basketball programs have a COMBINED 3 Final 4 appearances since 1990 (one each for Georgetown, Villanova, and Marquette).
In that same span, Duke, Michigan State, North Carolina, Florida, UCLA, Connecticut, and Kansas EACH have AT LEAST four Final 4 appearances (Duke and UNC 8, Mich St 6, UConn and Kansas 5, Fla and UCLA 4). Michigan State, North Carolina, and UCLA each have 3 Final 4 appearances since 2005.
Heck, Butler has two Final 4 appearances in the last two years, which means that by itself it has almost as many Final 4 appearances in the last 2 years as the entire "Catholic League" combined has in the last 20 years.
If you want SJU (and the other Catholic league schools) to remain relevant, then the only way to achieve that is to (1) stay part of the Big East and (2) for the Big East to remain competitive with the other power conferences in football.
This isn't the 80s anymore. I don't like it any better than you do, but we have to deal with it.