Maybe so, but banning the gun isn't going to stop it either. There are many more factors that need to be addressed. Poverty, access to good mental healthcare especially among teens. Teachers need to be trained on how to spot "troubled *******". Gun training in use and safety along with accident prevention should be required when purchasing a firearm. And again, instructors should be trained in how to spot "troubled applicants". Just a few suggestions.
I agree with the entirety of this statement. I would add that people with diagnosed mental health issues be stripped of their right to own a gun. Not unlike what we already do to convicted felons.
I have to run but I will try to respond to the rest of your post later.