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I don't.
One thing that bothers me is that with your system, the teacher most able to quickly stop the shooter would be the very one denied access to his gun. That gives the shooter that time advantage that they all use so well-- to kill as many as possible before armed response shows up.
One thing I've noticed, through experience, is that carrying a gun has made me much less impulsive. When you know the power to kill is at your disposal, little annoyances seem less important. True, some people aren't that self-controlled. Should they be in positions of power over kids with or without guns?

I agree, its a pitfall. That's how compromises work, though.

I'm sure there are freedom lovers who doubt that arming a few million additional public servants is the best approach...

It's not ideal-- but probably the best approach if you insist on imprisoning defenseless kids in a facility for much of their lives. The real solution is so obvious and easy-- and scary to people who confuse schooling with education.

They never consider that 'more freedom' could be the answer to anything; because they believe excessive freedom is always the problem. Disgusting.