Most of the shooters have been seen by psychiatrists, or should have been seen by mental health professionals. Even most determined gun rights advocates would not want a mentally unstable neighbor with an AK-47. As we can see most shooters are mentally disturbed people. If prevented from getting guns they would have ended up in a psychiatric hospital locked unit. Current practice of gun sales consistently fails to filter such individuals.
Mental health professionals need to be trained to determine risk of violence. If determined, mental health professional enters name into nationwide database. No gun sales to those on the list.
Generally, mental health system can do much more to protect society from violence and disturbance coming from sick, disturbed people who need help, not guns.