Lycoming in their 'Lycoming Flyer' recommend using the mixture to simulate a failure. I can't recall if was for m/e only, or included singles.
Their reasoning is along the lines of what Corporate Yank said: The throttle butterfly remains open so there is still mass airflow into the cylinders. This provides a cushioning effect on the piston and associated connections - as would normally be experienced by those engine parts.
Something else it might affect is carby icing probability with a closed throttle but fuel from the idle jet still evaporating, compared to no fuel being evaporated at all? Haven't a clue on this, really, but it seems to make sense. Unless the greater mass airflow with an open throttle has a greater temp. drop of course.
As for the general thread of the topic, I think a properly structured shutdown exercise is beneficial. There are many things we do while teaching that have some level of 'risk' compared to straight & level. I don't believe that a shutdown poses any greater hazard than some of those.
Similarly, I can't see that a shut-down in a fixed-wing is more hazardous than motor-glider or sailplane as long as the aircraft is operated within it's glide performance envelope.
Of course you don't expect the same L/D & therefore glide range, but what does it matter if you're operating within an appropriate albeit different performance envelope? As I recall, gliders could range from (very approx)18:1 up to a modern high performance sailplane's 50 or 60:1. This is a far greater performance change factor than that experienced between a C150/152/172 / PA28 etc.
As with gliding, once the engine is shutdown then treat the flight as commited to land. Judicious choice of an appropriate environment is needed just as it is for any exercise.