Shutting down the "wrong" engine is the classic error on a two engine type - there but for the grace of God!
Pilot Pete - agree 100% with all your comments - well put.
<you know it's coming and the instructor retards a throttle fairly quickly leading to the 'obvious' yaw, and you do have some time, although limited, from above<
The only comment I would have on this is why, during pilot training, the instructor has to retard the throttle "fairly quickly"? Surely all types of failure should be simulated and I would venture to suggest that it is a slow loss of power which, in many ways, is far more "challenging" to deal with in terms of identification, etc.
As an aside, my father (who is no longer with us) was a veteran light aircraft instructor/examiner and I always remember that he often would retard the throttle slowly to simulate a gradual loss of power. I remember sitting in the back of a light twin (Apache I think) with my father testing the candidate for his twin rating. We knew that the instructor who had conducted the training was always keen on "slamming" the throttle closed and when my father retarded the (hidden) throttle slowly this confused him somewhat leading to application of too much corrective rudder and then considerable difficulty identifying the "failed" engine. Some time was spent in the debried on this topic!
Finally, in many ways pistons are more complex with the added complication of pitch and mixture levers - there are a lot more "wrong" levers to pull compared to a jet.
RIP