Engine handling aside, it's all about risk management (God - I love those long words).
Because there is obviously a risk of mishandling when playing with simulated engine failures at relatively low altitude (and believe me I have had several situations where the pilot being trained/tested has caught me off guard by applying full wrong rudder during a simulated engine failure after take off) - it is safer to use the throttle method. But that is only my opinion - so it is a wise man that reads what the aircraft manufacturer has to say.
From the PA44 POH, Section 3, under Safety Tips:
Section 10 Report:
VB-860
Quote:
"Experience has shown that the training advantage gained by pulling a mixture control or turning off the fuel to simulate engine failure at low altitude is not worth the risk assumed, therefore it is recommended that instead of using either of these procedures to simulate loss of power at low altitude, the throttle be retarded slowly to idle position. Fast reduction of power may be harmful to the engine. A power setting of 2000RPM and 11.5 in Hg MAP is recommended for simulated one engine operation.
Unquote.
As far as I am concerned, that is good enough for me.
One other point. Part of the asymmetric training includes practice at identification. That will normally be done in the upper air where any mis-handling by the student is quickly rectified while at a safe height.
Only when the student is considered consistently competent at the identification process would one normally proceed to the engine failure on take off practice. This too, should be done initially upper air until the student is competent.
Once that is OK then part of circuit training will be the occasional simulated engine failure after take off. This is primarily a handling exercise as the identification process has already been thoroughly covered earlier.
The argument that pulling the throttle after take off makes it obvious which engine has failed, is valid - but does it matter? Not really, because the student has already demonstrated his identification competence earlier on.
The mixture cut is certainly realistic - but as the Piper people say " it is not worth the risk assumed" - and it is hard to argue otherwise. The ever waiting litigation eagle would presumably quote from the POH.