Engine off for training.
Way back in 1978 I (as an 18-year old) did my PPL at the West London Aero Club on PA-140's. The then CFI (DS) gave me a practical demonstration of shutting down the engine and doing an air-start both by using the starter motor and by a steep dive.
We were at a safe height and had Greenham Common below with a mile and more of runway to land on if the engine didn't start.
I must say the biggest thing I took away was a major boost in confidence. The aeroplane still flew, the vital actions to get the engine going work, and there was no need to scream, panic or freeze.
I never have had an engine failure for real but think that I would have been better able to deal with one if I did have one. In 1981 I had to shut down a dreaded Astazou XVI in a Jetstream as a precaution but that was in the cruise and a non-event.
Properly done I can't see the harm in demos of this kind in training, but do not advocate them being done in a test situation with an examiner.....
MB