In your world, greatly simplified, everything is black and white. Simply round up all the crazy nut jobs that might kill someone and lock 'em up. Simple solution.

Unfortunately, nothing could be further from the truth.

In the case of children who might commit violence, there is really no place to put them. They are shuttled to and from the local hospital until they calm down and are fit to be released to the parents. The parents take them home and hope, against all odds, that another "episode" won't occur again.

This process repeats itself time and time and time again. Even if the parent is concerned that the kid might injure someone, no parent will readily agree that the kid might kill someone, and, even if they did, there is no place to send the kid for a permanent solution.

However, once the kid enter the world of the criminal, due to any violence against a third party, there are plenty of facilities that will incarcerate the kid for an extended period of time...........after the crime has been committed.