I have used the switch to shut down car recently. I do not do it often. I mainly wanted to make sure it does what its supposed to do before going to the track.
Often, is a loose term. Modern electronics is fairly predictable, exceed maximum specs parts go poof. Years ago some parts could do more, now with well controlled manufacturing parts just meet specs. For the stator to get hot, two or more diodes have failed on the 6 diode bridge.
I am guessing, but I can imagine issues related to what Del said about load dump. If the alternator is putting out current, and battery pulled from circuit, the stator inductance will kick back resulting in high voltage. If the field is powered, but the ignition cut, the regulator, seeing voltage drop would up the field, resulting in overvoltage. While some imagine opening a circuit to cut power, when inductance is involved, the cut is not immediate, and the event leads to a voltage spike. Much like ESD, a very short term event results in damage.