Yes, I very much doubt that the average student would learn much more than 'monkey see, monkey do' during their PPL and wonder how desirable this is at that stage of the training, apart from over confident types, who may (or may not) learn that SEPs can bite hard.
Training later on makes sense to me, as it is easy to depart during avoiding action in the cruise and other scenarios.
Totally agree with the spiral dive recovery, since these are easy to get into and potentially destructive.