Entering autorotation in a helicopter is not simply a matter of throttling back the power until the aircraft starts to descend. If you do this, the blades will stall, the rotor speed will decrease, the blades will fold upwards and the aircraft to crash. To enter autorotation you must lower the collective to get negative pitch (or at least a very low pitch) at which the ROD airflow produces an angle of attack, such that part of the total reaction drives the blades forward. This keeps the rotors turning and keeps generating lift. None of these good things will happen if we simply reduce power in a propeller driven aircraft, because the mechanisms are physically very different. Your use of this scenario simply illustrates your lack of knowledge regarding helicopter POF.
Keith, that is a big strawman, and not your first. Nobody has said that entering auto is a simple matter of throttling back the throttle
What I wrote was that your description of what constitutes THP implies you would be in auto as soon as Thrust x RoD (equivalent to T x TAS) exceeded profile power, when what actually happens is that auto begins when RoD exceeds induced velocity by enough to offset profile power. This is a fact.
the mechanisms are physically very different
The actual mechanical arrangement is superfluous, this is about the over-arching physics. Simple momentum theory considers only that a 'disc' accelerates air. This does not tell you if the model is mechanically capable of going into auto, it tells you the theoretical relationship between induced velocity, RoD and thrust.