I'm told a PPL no longer requires spin training. Does ATPL?
Without looking it up and if I remember correctly, only the CFI rating requires a demonstration of spin recovery.
The point is that if pilots do have a fear of stalls/unusual attitudes (they do - I have witnessed it) irrational or otherwise, then the best place to confront that fear and learn to control it while applying correct recovery technique is in the simulator. Current simulator training on imminent stall and unusual attitude/upset recovery tends to be treated as a handling warm up exercise before getting down to the serious work of flying approaches and dealing with systems failures. IMHO if we allowed pilots to experience full stalls and how to recover from them safely in the simulator that would be the best preparation for mastering correct recovery technique from an imminent stall.