I’ll speak for Nova first... well known for men’s and women’s running. Multiple national titles in track and cross country. Nova also has one Division 1 football title. I think outside of hoops Nova has more championships than UConn.
Nova has more than twice as many NCAA national championships than FSU. Not bad for a little private school.
In hoops 4 of the 11 current members have national titles. UConn, Nova, Georgetown, and Marquette. All members have been to the Final Four except newcomers Xavier and Creighton.
Lacrosse is respected. Denver is an affiliate member and has a Big East national championship (and 32 other titles in skiing and hockey).
UConn, Nova, Georgetown, St Johns, Prov, and Denver all have titles in other than hoops.
So yes, we are a basketball-first conference no question. Our members, however, have achievement outside of hoops.