the problem comes in when you, as BBB stated, mix guns with stupidity.
What we need are comprehensive, secure background checks, better treatment for the mentally sick
You didn't really read through what I posted above, did you?
"Mentally sick" aren't stupid and aren't deviant either, they may coincidentally be all three and even then doesn't mean they are going to murder somebody.
there is no proper background check for "stupidity", and there's plenty of people with degrees that are stupid, so how are you going to do "background checks" for "stupid"?
Here guns aren't highly restricted, you won't get guns because you've cleared yourself from restrictions, it's not normal for people to own guns, period. Yes there is a black market for guns, that doesn't mean every damn person is buying guns from the black market, most people buy guns legally, the ones that are allowed to of course bc they're either certified collectors (to buy collectors items) or pay to have hunter's license. There are still guns, but most of those people with them are usually employed on agriculture/own farm terrains and do occasional hunting, they do not need to commit crimes (besides embezzling with european money for not growing crops or owning grazing terrain). Yes there are some rare crimes that include guns, recently there was one that the robber forgot the gun at the scene yet it was a replica, just to give you an idea that people don't really use real guns lol. The most famous recent robbery of "value trucks" on the inter-state was done with pickaxes and a handgun, known here as the "pickaxe gang robberies". The most famous ATM machine robberies were done with gas-leaking explosions, no guns involved. Yes now and then, specially with drug trafficking, they bust large arsenals of blackmarket guns but gun violence is extremely low, maybe it's because they know the people they deal with don't have guns, who knows.
Point is, mental health can't be the blame for all or even most of the gun violence in USA, and you can't background check for stupidity. Neither mental health or stupidity are requisites for crime and gun violence, study deviance and you'll see it isn't, it's much more often the result of social conditions, which when improved, lower tendency for deviance.