I really don't believe too much about the Big East really being on the downturn, but instead possibly just evolving into a solid basketball-only conference with schools having that same vision. The schools in the Big East have not only had consistently deep NCAA tournament runs, but many also with championships. In some regards, when compared to the ACC, SEC, Big 10, or Pac 12, the schools know their identity: basketball schools. I can see that appeal to Shaka, especially given his roots as others have mentioned.
As much as I've been happy about the rise of the A-10 over the past few years, rarely has a school consistently gone deep in the tournament; and Butler wasn't in the A-10 long enough to count in my opinion (and wasn't a member in their back-to-back championship appearances). There's always a solid team or two, but rarely one that has been able to maintain a strong NCAA presence. Similar to the feeling with Calipari at UMass, I never really felt Shaka was at VCU for the long term. In fact, I'm not even sure how the A-10 will shakeout over the next 2-5 years. There are nine private and four public schools, UMass the only school with an FBS program (although not exactly established; but would be surprised if their long-term eye isn't on the American Athletic Conference), and speculation of VCU, Saint Louis, and Dayton leaving at some point. I can definitely see Shaka going for the Big East, and Marquette seems like a good fit for him.
I suppose the question of why Marquette over BC, Wake Forest, Illinois, and UCLA.....but Marquette seems mostly focused on basketball out of those schools and, as others have said, he has his roots there. The fit seems natural and the timing probably as good as it will get.