Personally I think, in general, flight training over overemphasizes the spin entry and recovery and underemphasizes spin avoidance.
The accident sadly shows that most inadvertent spins occur at low level and no amount of spin recovery training would have made any difference as there was simply insufficent height to regain controlled flight. In Canada the requirement to demonstrate spin entry and recovery was removed from the flight test. A spin lesson is still required but I use it to show what happens if all the warning signs are missed. But the bottom line is simple. The airplane can not spin if yaw is controlled in the stall. Using the rudder to control yaw must be an automatic part of the stall recovery and occur at the same time as the nose is positively lowered and full power applied.
Similarly recognition of the slow flight regime is required in order or avoid stalling.
So if you get into an inadvertant spin then you were IMO stupid times three.
First for inadvertantly getting into the slow flight regime, second by letting the aircraft stall, and third by not controlling yaw so that the aircraft departed into a spin.
With respect to damaging aircraft in spin training I have seen two C 152's with bent horizontal stabilizer spars. Both were the result of a spin going into a spiral dive followed by an aggressive pull out at high speed.
One good trick is to not have the student leave the trim at the cruise setting when entering a spin. If the aircraft is trimmed for slow flight and it spirals out
the aircraft will try to regain the trimmed airspeed which will be much slower than the speed out the bottom of a spiral dive. This will cause a strong pitch up force on the control wheel and IMO contributed to the tail damage described.
When doing a walk around I always have an extra good look at the horizontal stab as that is what is likely to be bent if the aircraft was abused.