Unfortunately, it doesn't always work that way for the midmajors.
After Steve Alford left Missouri State, they took a step back with Barry, and now he's gone and they are an abysmal team.
After Keno Davis left Drake, they are mediocre, and rebuilding.
After Turgeon left WSU, they are struggling to rebuild, too.
In fact, other than the success SIU had with Painter and then for a couple years with Lowery (not now, though), just about every other example you can find in the MVC of a coach being hired away was followed by some pretty lean times, and not much success.
Many other schools like Winthrop, UW-Milwaukee, etc. may take a long time to get back to the levels their former coaches had them at.