I've never, as a fan, not wanted to see a postseason game. I would gladly accept a CBI invite, the more games the better. Not the other way around. These kids aren't going to "rest" this summer, they're going to play more basketball (or baseball). Might as well do it with an STJ uniform on.
Also, St. John's can't be invited to the CIT. That tournament is for smaller mid major schools only.