While it seems a good idea to inject realism into training for engine failures after lift off in single engine aircraft, the manoeuvre conducted necessarily at very low altitude requires almost instantaneous decision making by the student. There is precious little leeway for error before the instructor is forced to take over control to salvage a wrong decision made by the student.
It is important the instructor does not spring a surprise on an unsuspecting student which is why it is wise to have the instructor call "Simulated engine failure" just before he closes the throttle to idle. At any subsequent court of inquiry in event of an unfortunate ending to the practice engine failure on take off, you can be sure the insurer's legal team will try their best to nail the instructor for the cause of the accident. After all he is pilot in command.
A simulated engine failure on take off should be made at a safe and reasonable height where the student has enough time to make a considered decision where to force land. Usually it is straight ahead preferably into wind apart from a minor turn if needed. In other words if the instructor is required to assess if the students decision making is safe enough before first solo, then sufficient altitude needs to be allowed for the instructor to assess accurately. The instructor has responsibility for the safe conduct of the flight and this will be a vital point of law if any accident is the result of poor instructor technique. Example being a quick closure of the throttle without first warning the student. Especially at low altitude where there is not much room for error.
if the aim of the sequence is to have the student land straight ahead on the remaining length of runway, then the student must be previously warned that is the purpose of the exercise. In every case the instructor must say Simulated engine failure" before he closes the throttle.
Depending on terrain and obstacles, 500 feet above airport elevation is a reasonably safe minimum height to commence the engine failure after take off procedure. That allows the instructor time to reasonably assess the students actions and allows the student the time to make a considered response. Anything below that altitude increases the risk factor of mishandling and the increased likelihood of instructor intervention.
You cannot protect the student once he goes solo. On the other hand the instructor must be aware that his action of pulling an engine on his student at very low altitude needs to be balanced with its training value. Increasing the risk of mishandling does not equate to better training value.