Again my observation of people's behaviour suggests that the most likely cause of the power loss is due to lax operation of carb heating
Yes, this always amazes me - a lot of people around where I am treat the carby heat as if it should always be locked off, even though the conditions (often very humid air and usually somewhere between 20-30 degrees C when airborne) are perfect for it.
Unfortunately the autorotation entry as normally taught is much slower than this scenario and unexpected complete shutting of the throttle discouraged.
I agree totally on the importance of making sure the lever goes down as quick as you can - the POH says not to do throttle chops because of the chance of the student doing the wrong thing or the engine stopping, but it's certainly a massive difference between a gentle coordinated throttle roll-off while the lever's going down and what would really happen if the power suddenly went away with the collective up, not to mention the oh **** factor.