I think this is academic for most pilots, but yes it's very true that you can pull harder and recover with less altitude loss by applying power ASAP. Most airplanes will also stop the spin rotation more quickly with added power than without, but this is not a good technique to teach as emergency spin recovery technique. As far as minimum altitude loss goes, you can even take it a step further and say that you might be better off letting the spin continue to 3/4 of a turn than trying to recover immediately in the first 1/4 turn. Applying recovery inputs at 1/4 turn will have you stopping after about 1/2 turn, which puts you in the steepest on-your-back attitude, which requires the most amount of pitch change to return to level flight. Recovering such that a full rotation is done will put the airplane at the most nose high attitude with the least amount of pitch up required to return to level flight. I've done 1/2-turn and 1-turn spins in the Cub and Pitts trying to recovery each with minimal altitude loss, and the 1-turn spin recovered with the least altitude loss for both. You can recover a 1-turn spin in the Cub in about 350 ft.
Again, all this is mostly academic since pilots who are spinning accidentally in the pattern are unlikely to have the skill or muscle memory to recover so quickly or have the presence of mind to monitor the degree of rotation. I think those who have the skills are not going to go around with much of a chance of spinning in the pattern accidentally. I think everyone should get spin training, but I do not think it's practical to mandate it for PPL training, since there are too few truly qualified instructors and suitable airplanes to make this happen across the board. For dedicated acro/spin instructors, spin training is very safe.
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