Interestingly, one of the largest obstacles that prevents background checks from being as effective as they could be is……government regulations. HIPPA makes the medical records of a mentally ill person so confidentially protected that they can’t be accessed by either background check or law enforcement.
In many ways, accurate background checking is the victim of our own penchant for personal security. Instead of letting information on a “need to know” basis, the law is written “no way, no how”.
So, stuff like that, rationally eliminated as an obstacle, would have some mitigating impact on the problem.