While there may be some emotional satisfaction in seeing a member of management being required to "wait up" for me....as a practical matter I would much prefer the sup to go home, get a good nights sleep, get to work a few minutes early the next day, and fix whatever problem it was that caused me to be out late the night before.
You dont fix dispatch problems at 7:30 at night. You fix them at 6:30 in the morning.
I assume you were kidding. No matter what time they leave, nothing different will happen at 6:30 the next morning.