I guess the logic is that people with little experience will likely freeze under stress unless there is a clear, programmed response to the stimulus.
You're absolutely right. There's an old saying that "how you train is how you fight," meaning what's done on the training ground is replicated under stress in the field. Police officers who are used to picking up their spent brass on the shooting range have been known to inexplicably do the same thing in the middle of a gunfight, and get shot in the process. It falls back to what's known as the law of primacy; what's first learned is first remembered, and it's also where we go when we are under stress. It reinforces teaching things properly the first time.
I fall back on that in primary instruction when in an airplane such as a Cessna 152, my initial instruction involves one airspeed; climb at one airspeed, approach to land at one airspeed, and use that same airspeed in the event of an engine-out. We later begin to expand on that and explore different ways of configuring, climbing, approaching to land, etc...just as a student expands into learning soft and short field takeoffs and landings, slips to landing, no flap landings, etc...but everyone has to start somewhere, and learning habits that are crucial to survival in an emergency are important.
That said, many pilots today aren't properly taught that there are two important glide speeds; one is best glide distance, but the other is minimum sink...many students are never taught about minimum sink, and their instructors probably aren't familiar, either. These in turn are important in understanding the drag and power curves, which help explain performance throughout the flight range. Understanding these and how they apply to your airplane help understand what's going on and maintaining situational awareness in unusual or emergency situations.
Perhaps the challenge is how to handle the crossover stage, e.g. the point at which the pilot has enough experience to start to think clearly as you decribe.
There's an old zen philosophy that when one undertakes the study of a flower, it's just a flower, As one's study progresses, the flower becomes more than just a flower. When one has mastered the flower, it's just a flower again.
The "crossover stage" is really an on going evolution in which we are all a student. How we understand it changes with time. A wise man once said that the best part of growing older is that we get to experience the same things from a different perspective.
I would submit that while the goal is always mastery, and therefore making the flower just a flower again, one can never let go of the concept that there is more to be learned, and more way to learn it. It's a process that can't be rushed, but should be approached with caution, always remembering that the flower is more complex than one may realize. It's with that in mind that one can really come to appreciate the beauty of what we do, which is to perfect flight. It's a job which is never finished.
The perspective is a little hard to see in this picture, but the bottom of the side canopy door hanging down sits about six feet of the ground. The hilltop behind the airplane is about 9,000', and the elevation of the resting site is about 5,000' above sea level. The aircraft was actually stopped by the wood piling up between the main landing gear, and other than a collapsed tailwheel assembly, no other damage occured (beside the toasted engine, which was done before the aircraft ever reached the ground).