This would be a very big concern for me too.
This is also a world in which police officers sometimes shoot the wrong person, maybe not even accidentally but due to prejudice. JMO. There have been cases here on WS where lots of mbrs here say that police officer should never have been an officer. Yet he/she (usually 'he' I think) was.
Even though anybody (including a teacher) who shoots a school-shooter and saves students and teachers, will probably feel good about that, they may also feel 'all sorts of other stuff' and need psychological help afterwards. Police officers and soldiers etc are trained for that, teachers aren't. Apparently the act of killing someone can be enough to give a soldier ptsd, called 'perpetrator trauma'. What about a teacher? You might not want to call it 'perpetrator trauma' because the teacher was trying to protect people, but that wouldn't stop them from being traumatised.
What happens to the teacher who could've shot, but didn't? Will they be charged?
I think the idea of arming teachers is opening up a minefield.
I can't name my solution here and unfortunately I don't think it will ever happen in the US.
JMO MOO