Going back to "Up in the Air's" post. Generally I agree with the statement to follow the POH. However, it should be noted that they vary a lot. I think if you look at a training twin like (say) the Travelair POH it is completely different on this subject.
One of the deficiencies of this debate is that it hasn't acknowledged that there are different types of twin engine engine failure training.
At one level, recurrent training is about re-inforcing the checks and establishing the mechanical routine required in an engine failure. Simulators can do this pretty well and should be part of the strategy.
Statistically, the most likely scenario is an engine shutdown in flight. But in this instance there is plenty of time and its not so critical. You can pull out the POH checklists. This is where you need the feathering exercises. It proves that the aeroplane will continue to fly very happily on one engine.
The two most critical situations are engine failure in an instrument procedure towards the MDA involving a missed approach and engine failure after take-off.
Engine failure after take-off (or indeed go around) is critical because if you don't act swiftly, decisively and precisely then some twins won't climb on a single engine. Its also a high workload situation where the pilot is most likely to mis-diagnose the failed engine. I'd suggest that the new multi-pilot's first experience of this ranks with the first solo as a memorable experience. This cannot be replicated in a simulator. But proving that if you get everything right you can climb for a circuit at 150 fpm is a very big lesson.
EFATO may be an exercise which carries risk, but so do many other things. The issue is how one manages the risk. I would argue that an EFATO exercise that requires the pilot to go through the checks feather the engine (ie the instructor set zero thrust) and establish a climb is an exercise best done at a country airport with flat terrain. If the objective is to identify the dead engine and do the checks before the instructor restores the engine, then the circumstances in which this is done is less important.
I'm part of the school that still thinks stall / spin training is important. Ditto, I think the experience of a simulated EFATO at low altitude done once is indelibly etched in the memory and an important part of multi training.
But, after the first experience the check rides are about re-inforcement of the correct routine. Every time I do a sim flight I fail an engine on myself. I'm going to hit any instructor who pulls one of my turbo engines at full power on first take-off and like most turbo engine owners we avoid circuits. But pulling an engine toward MDA in an instrument approach after the engine has been at low power for a while is much kinder on the engines and still lets you do the climb transition in the go-around at 1,000 ft or more above the ground.