and, after the student has continuously demonstrated a high proficiency standard of handling such emergencies at altitude.
Could you give more detail to the words "continuously demonstrated". How many practice engine failures at `altitude` would you say were needed in order to demonstrate ` a high proficiency` Maybe five, ten, fifteen or even twenty? In fact there is no figure, is there? If the student does a good job of it two or three times then he is competent and has demonstrated high proficiency.
If he then shows the same proficiency when conducting a practice engine failure shortly after take off then there is no point in thrashing him time and again with practice engine failures after take off. You are wasting his time and money. There are those instructors who simply love cutting engines after take off until such times the student makes one cock-up on identification or procedure and the instructor says "GOTCHA BY THE BALLS THAT TIME MATE" And that is the excuse he needed to do more and more engine failures until the next mistake and so on.
As one Ppruner replied the sequence of engine failure after take off is fraught with danger (unless it is in a flight simulator). If the sequence is conducted with the usual precaution against mis-handling it is not `fraught`with danger anymore than crosswind landings are fraught with danger. Having said that I agree that cutting the mixture to simulate engine failure after take off is indeed fraught with danger since a real engine failure has been deliberately induced rather than a simulated failure caused by throttle closure. Big difference and one which has caused loss of lives.