there's not a theoretical justification to think that the aircraft should simply sort itself out.
This is key...
Most every plane I fly, I stall - numerous times, and in every configuration. I continue to be amazed at the variations in handling, and "sorting itself out" which I experience. Some are great, a few marginal, and one recent (Italian type certified) one did not enough pitch control available to prevent a stall in certain "normal" configurations. I like to find these little surprises with lots of altitude, and all other things being in hand. EFATO is not the time.
As obviously does the OP
, if you commonly fly one or a few types of aircraft, it is excellent to cautiously experiment (with mentoring, if appropriate). The more you know about what your plane will do, the safer you'll be.
There have been remarks about stopped propellers, and the differences in drag. Yes, this is often the case, but I consider this risk to be well down the scale. For my experience, though failures of engines to develop useful power occur, seizures are rather rare. If your skills are good at handling the aircraft with an idled engine, the differences you could experience with a stopped prop will not be so different as to invalidate your skill.
Then there are the really odd situations.... Last week while flight testing a Piper Cheyenne II with an external survey modification, the left main gear decided it was very happy staying in the wing, despite my seletion for it to appear. After the methodical checking of systems, and repeated attempts, but before going to full blown emergency procedures, I decided that a few G's might coax it down.
Though I can happily find a bit more than 2G in a coordintated turn in most aircraft, and anger it closer to 3G by pulling once there - not it a Cheyenne! At speeds appropriate for the gear being extended, and with the flaps up, it gives an unmistakable stall buffet before you get to 2G. Two attempts at that were enough to convince me that fooling around accelerated stalls in a Cheyenne was not for me! Though perhaps it helped, as shortly afterward, the gear presented itself as desired, and it all worked out in the end.
It is easy to see that when something goes wrong, pilots can lose track of the primary role of mantaining controlled flight, and the problems compound. Engine failure during climb would be one of these opportunities. That probably factors well into the points with Big Pistons has presented, with which I completely agree!