While also benefiting the million students in despair, who share many significant traits with the FBI standard issued 52 page school shooter, that aren't violent?
For every shooter there are a million mistreated students, who choose to suffer in silence. So it will take a lot of effort to reduce the amount of very fringe outsiders, who can commit the willpower to kill their own peers, but somehow lack something to use this willpower to improve their own situation in a positive way.
I like your general rule and there is actually no simple fix. But there are simple things you can do, that improve a situation a lot.
Making schools less hateable isn't a bad idea and probably easier to achieve, then getting rid of all available weapons and everyone on happy pills.