GRpr. The fundamental reason why mixture cuts to simulate engine failure after take-off are risky, is that you have actually failed the engine. In order to restart it, the throttle has first to be closed. Then the mixture has to be moved from cut-off to rich. Finally, to restore full power you have to advance the throttle. With six levers all in a row, that is two pitch levers, two mixture levers and two throttle levers, there is a danger of confusion between instructor and student as the student carries out touch drills and the instructor resets the mixture control and throttle lever.
The possibility of confusion is reduced if only one lever (the throttle) is used. Also in event of gross mis-handling by the student resulting in the instructor hastily taking over control of the aircraft, there is instant power available from the throttle.
Make no mistake about it, if you intend to take up multi-engine training as an instructor, sooner or later you will get the fright of your life caused by gross mis-handling by a student. You may not have time to recover the situation at very low altitudes.
It is not uncommon for the student to apply full wrong rudder to prevent yaw as the engine fails. Things happen alarmingly quickly then, and you will have your hands full - especially if you have cut the mixture for "realism" and you do not have enough hands to fly the aircraft while at the same time trying to get the engine started.
When you called "Taking over control" to the student, he would have relinquished all control pressures including the rudders. As his instructor, you are now all on your own trying to salvage the critical situation of your own making.
There was a fatal accident in a Partenavia when the instructor cut the mixture at 100 ft agl after lift-off. The student was caught by surprise and the propeller windmilled. The aircraft lost airspeed and the instructor attempted to re-start the engine at the same time he took over control.
It was all too much for him and the aircraft clipped power lines 100 metres from the departure end of the runway before crashing into a house. The crew of the Partenavia survived, but the 3 people in the house died in the conflagration.
Some Regulators have banned mixture cuts at low altitude. Others such as the Australian CASA leave operational decisions to the instructor. Regarding practice feathered landings, the Royal Australian Air Force banned those 40 years ago following a spate of training accidents which wiped off several aircraft.