In terms of spinning, there are three types of certified, single engined GA aircraft: All have demonstrated one turn in and one turn out, but maybe with considerable skill, and no reserve. A few are well designed to be spun and recovered = aerobatic types, and a small group of compromise aircraft which can be safely used for spin training, but are lackluster in handling - usually because their design errs to the safe side. The 172 is in this category. It is a massive compromise, but a compromise which has worked.
A 172/152/150 can be used for spin training, in it's basic form. A pilot competent in spinning those has spin recovery awareness, which is much better than none. I expect it's likely that pilot could spin another type, and with only modest skill, have to really work at getting out. But I opine that a pilot capable of recovering a spin at all, is better than one who cannot at all. They have a hope, if upended in a plane.
All of the formal spin training I received was in 150 and 150 Aerobat only. Does that training make me a well rounded "spinning" Pilot? I think not. If someone spun me up side down, in a quasi military or aerobatic training, I expect my skills could be exceeded - but I would attempt a recovery based upon the training I have - that's better than nothing. Although I have abused some spin recoveries, I have never deliberately explored abused spins. I'm a "one turn in then one turn out" pilot.
But I have practiced that lots, and demonstrated it on many types. My broad experience (not deep, broad) with many types tells me that a Cessna 100 series spin trained pilot, who practices, and applies themselves, can affect spin recoveries in other types, which are much less forgiving.
One of the nicest recovering types I have spun; Lake Amphibian. A couple of the least nice; Cessna 206, and 185 floatplane. Requiring the most precise recovery technique (to prevent exceeding limitations); Cessna Caravan - though it did recover well. Most viscous entry (unintended) DC-3. Non-event spins; C 182, and as amphibian, 150HP C 150 taildragger on wheel skis, Citabria on floats - and Ercoupe (but you can't hold it in
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In a competent training environment, spin training in a 172 (or 152/150) is much better than no training. It is incomplete, but better than nothing.
And... and aircraft which recovers a spin to a spiral dive on its own, does provide a valuable and different aspect of training - recognizing changes in condition of flight which may be uncommanded, and reacting accordinaly.