Couple of problems with your solution. First I am one of those constitutionalist dudes, the right to bear arms was meant as a solution for the common citizen to fight tyranny, blocking this right would in turn be in favor of the possibility of tyranny. However blocking an individual from obtaining weapons so that they don’t harm others (mental health, drug, violent histories) would be more in favor of Locke’s universal laws of man (and women) which the constitution was based on, at least in part.

Second in response to your weapons to cars analogy, and as someone who lost their gun loving gf to a car accident (so admittedly some bias may be involved), I am well acquainted with the reality that gun violence makes a small fraction of all violent crime you would be more likely to die as a result of some one stabbing you with a knife or even with their bare hands, each as their own statistic, than with a gun. This is because most violent crimes occur where the victim knew the murderer and it was a crime of passion (legal term where people get heated and act in the moment), so you’re more likely to have a friend or family member strangle you over a game of monopoly than a stranger gun you down with an ak47, statistically. However despite this people are even more likely to die in a car accident, more often from not paying attention than drunk driving believe it or not than any violent crime, so you are more likely to be killed by some txting “do we need milk?” And hitting you than someone trying to strangle you over monopoly (its a tough game that can destroy friendships haha). The only thing topping car accidents would be overdoses, more on legal prescription opioids than illegal narcotics. I would like to point out that both cars and access to certain classified drugs (ones with high abuse/addiction potential) are privileges which are legally more easily restricted and yet we don’t have a handle on that.

What we need are two things which while not easily legally enforceable are seemingly lacking in modern society. First is more personal responsibility among individuals, its lack can be seen in the highly litigious nature of modern society where we quickly look to pass blame on others for our own stupid actions. If you read the warnings on a plug in window ac unit they are required to say that if they fall from a window they could cause injury or people, animals, or property because someone dropped one got hurt and sued, where securing it should be the responsibility of the ac unit owner. Second is social responsibility, which is fading due to highly aggressive pc repercussions from those around them. People are afraid to report things that could harm others/property for fear of being not pc. Evidence can be seen in the recent terrorist shooting in CA shooting where a neighbor saw they were receiving tons of boxes, worked late hours in their garage, and had people constantly going in and out of their house however didn’t report it for fear of being labelled a racist. For all we know they could have been running a meth lab in their garage (the wife was a pharmacist or so they say so she could plausibly have been Walter White, the husband would be Jesse Pinkman) which aside from the obvious of how bad meth is for a community its production is highly toxic and a massive fire hazard, which would be doubly dangerous given how dry CA is.

Off the top of my head the ways to possibly enforce or encourage this type of behavior we are lacking would be to one make a federal registry of a sort that tracks informal sales and make people of last register who sell their guns that appear in crimes criminally accountable as a lesser degree accomplice (still would see jail time). As far as social accountability we could offer rewards for people that describe a very specific crime and report the individual which we then investigate the reported individual for that crime and that crime only. That exists to an extent but by adding a positive reinforcement it could further encourage the behavior (say what you want about BF Skinner, positive and negative reinforcement work). We do not need to make it hard for people to get guns who don’t need to jump through hoops because as you said ultimately when someone wants something they can’t otherwise obtain legally they will pursue it on the black market.

Lastly for, the record I don’t own any guns, nor do I plan to in the near future.