There might be something there which these schools could harvest.
That training is about taking people out of civil society and giving them the ability to engage in behaviors that would give others (quite rightly) pause. This is not a place to look to generate well-rounded citizens that do not see violence as a way to manipulate others.
I have never been in the military, but I've training Brazilian jiu-jitsu and some mixed martial arts for many years now. Practices can be tough.
I'd guess they don't take it far enough to be useful. When people first experience cold, hunger, fear and exhaustion, most focus on their suffering, and feel helpless. You can learn to take the discomfort for granted, focus on your actions, and feel proud. That takes more experience and mentoring than the average student gets.
Also, being able to handle the normal stuff is good, but not caring about it at all is bad, and the middle ground can be hard to find. Tim Winton's novel, Breath, develops that idea.
Do yourself a favor and read Judith Herman's book "Trauma and Recovery." You'll quickly understand why your counter-intuitive observation is simply wrong. These things work in special forces training in a way they never could and never will in prisons and hospitals.