I recall one accident in a light twin where the prop came off one engine, spun over the top of the airframe and ripped off the other engine. Instant, massive, aft C of G change, loss of airspeed and spin entry.
The pilot was ex-military; he recovered from the spin and landed in a field.
No "recovery at the incipient stage" training would have saved his bacon.
You can be trained to avoid "spinning" in a car. But if someone clonks your car into a skid, you'd be better off knowing how to deal with it. Everyone agrees that "skid pan" training is a good idea, don't they?
The thought of trying to recover from a spin in an aircraft without having been trained how to do it, or perhaps even without having seen it?....... no thanks.
I'm pleased to have been able to learn how to ride a motorbike and drive a car in wet, muddy farm fields, where skids were just part of the deal. Similarly, my military flying training introduced spinning quite early on in the syllabus (actually, it was still formly in the syllabus of the PPL back then in the early 1970s, which I completed).
Then almost every military GH training sortie included at least one spin. Pilots are of course also trained how to avoid them. You'd need to be very lucky to recover from a spin on short finals, flaps and gear down, etc. Irrespective of who trained you.
Rotary training also included full down EOL autos. You needed to be good at it because the rules prohibited re-engaging the engine for go-arounds once the throttle was closed. Again, not many PPLs get to do these to the ground.