Well, quantitative measures would say it’s a top 3 conference.
So your list is Seton Hall, which really was more mid tier historically and not a bottom feeder. As a BE member they did make the finals.
Your other example of a current championship contender is Prov because they finished 4th. I wouldn’t call Prov a historic bottom feeder, or a recent championship contender. So that is weak for your list.
Now, for recent bottom feeders that were former Big East contenders we could talk about UConn, Pitt, and BC.
The Big East has Nova, Georgetown, St Johns, Seton Hall, Prov, and UConn. That’s a pretty classic core of the conference.
WV, Ville, and Cincy were short term tenants.
Pitt was a contender but never went to a FF as a conference member. Prov and Seton Hall did.
Cuse is a nice foil. I’d like them in the Big East, but I’ll pass on the other former members. UConn rejoining is great for the conference. I’ll pass on the rest.