I only do engine shutdowns in the summer because I hate doing top overhauls and buying cylinders...just kidding
but seriously my school was a MI school so we always tried to balance shutdowns with minimizing damage. Hey, when you pay the bills you have to. I use 5K over the airport.
I also remind them that we are operating under the premise of a cruise engine failure in this scenario. You've got time and performance. If they get the impression/misconception (based on cruise, driftdown, etc) that they are going to climb on Takeoff in a Seminole, Dutchess, Seneca, etc. They are sorely mistaken.