I think the B1G is looking for a bunch of relatively easy, but somewhat respected wins based on the names on the uni's.
While the Formerly Big east had a lot of teams in the NCAA's and the MVC only had one, the one MVC team probably got more respect, attention, and media articles than the entire Formerly Big east.
The Formerly Big east lost their FB schools. Those were the ones who gave the BE most of its attention. Recruiting to the current FBe members will probably drop off a bit when they can't guarantee recruits games against the FB schools.