All the mental health screenings and background checks won't make a lick of difference so long as there remains a vast, black market for buying guns in this country. If sociopathic revolutionary wants a gun, then sociopathic revolutionary will find a gun.
It remains an unanswered question in these debates:
If the number of legal guns out there decreases, AND the sale of guns are tracked and audited from manufacture through wholesale to retail and thence to private sales, AND the act of carrying an illegal gun results in destruction of the gun and stiff penalties
then where are on earth are you proposing that these illegal guns come from!?
The number of illegal guns out there is directly a result of lack of oversight on the gun inventory.