I ALWAYS shut it down when switching riders because I don't see any reason to leave the engine running, and plenty of reasons to shut it off, such as:

Peace of mind for the rider coming in that the prop is not turning.
Reduce the CO at the back of the boat. Who wants to breath CO while putting their board on and getting ready to ride?
Saves gas.
Saves hours on the boat.

Even if someone is using the heater, I still shut it off. My Perfect Pass powers back on and remembers the set speed before I key it off so no issues there. Just fire it up and go.

Al