Background checks have been around for decades and get tweaks but some problems stay the same or get worse. This should be a hint that they are not effective measures. I would even argue they are counterproductive by doing things like stigmatizing mental illness.  If you cannot find or treat a problem then attempting to screen based on that problem is ineffective.  Background checks are single time point events so if something changes that check has little value. You have no control over future mental illness.  I have known felons who had guns for hunting are ranch work. A mistake in youth should not condemn a person for life.