We were talking about this at work over the last couple of days. We older people remember when there were mental hospitals, and we agreed that some people need to be in that kind of facility. Not locked up in a prison type place, the local one was like a village. The patients had jobs if they could do one, there was a store, and they were made to take their meds. If they walked away, the police took them back.
Now a lot of these patients wind up in prison after going off their meds, and others, like a friend's daughter, get involved with law enforcement every so often after going off her meds because she feels "dead inside".
Thinking back to when I was in school in the '60's and '70's, there are only a few teachers who I thought were stable enough that I would have wanted to arm them. The younger people feel the same way about the teachers from just 5-7 years ago, so I'm assuming that it's across the board. I can think of 2 of my grade school teachers I would be okay with arming, and another 3 in high school. Of the 3 armed (They concealed, badly) security officers we had in my high school, there was only one I thought was sane enough to carry. The other two were overly aggressive bullies, both ex HS and college football "heroes" that were hated by many of us kids. There was another male teacher I thought was ok, and a couple of female teachers. This was about 10% of all the teachers I knew.
I think the solution to reducing these incidents is to put a cop into every school. Yes, it's expensive, and it won't be a sure thing, but it would probably reduce the chances of it happening, just by his being there. A couple, just a couple, of armed teachers would be a help, as the police officer would be a logical "first target" for a shooter to take out. No matter what is done, there is no way to totally prevent this kind of thing from happening. If someone decides to go on a one way "mission", it's going to be very difficult to stop them with a law or reasonable security procedures. But myself, maybe because I have no kids in school, I don't feel the odds of it happening are sufficient to warrant spending a ton of money on security. Schools are in general, very safe. Get rid of glass doors and large windows that can be shot out and passed through, put cameras at the right places, and use common sense, something that appears to be in short supply anymore.