> The only thing we need to fear is crazy people who have guns. And that's a relatively easy problem to address: require thorough mental and background checks for anyone who wants to buy a gun.
This statement contains at least two problematic assumptions:
1) Only people who have committed violent crimes in the past will commit them in the future. (see: "background checks")
2) People who are mentally ill are inherently dangerous, or at the very least "could be" (see: "mental checks", "crazy people")
The problem with (1) is that a background check will not reveal very much for most folks. Sure, if you've got a lifetime of criminal mischief, a felony or two, that will show up. But that time you argued with someone and threw a brick through their window, but the judge let you off with a "public disturbance" - not gonna show up. For the vast majority of the country, a background report would not be a useful or helpful qualifier. For the worst of the worst, we can't pretend a black market on guns doesn't exist, so it would not help there, either.
The problem with (2) is that you have now decided to deny what is otherwise a fundamental right, guaranteed in (an amendment to) the Constitution to all citizens of legal age. Your logic for stripping a large number of citizens of this right is that some of them might do bad things with it. There is no clinical diagnosis for "is likely to go apeshit and shoot someone" - in fact even among schizophrenics there's no clear indicator of "violent tendencies", let alone an actual predictor.
Another problem with (2) is that you assume that mental health is constant throughout a lifetime. If I'm 18 and go in for a comprehensive mental status evaluation, I may come out just fine and start buying guns. But what happens if I present as Bipolar at 30? Schizophrenic at 40? Do you get to come and take away all my guns at that point? Should that be the duty of a psychiatrist - to determine who is allowed to own weapons? What if the psychiatrist gets it wrong, are they liable? Even if we assume somehow a psychiatrist was able to make that diagnosis and be right 99% of the time, you've now introduced a fairly major reason NOT to seek mental health care - they may take away your guns (or prevent you from getting one).
Sadly, throwing out "it's only crazy people with guns" is a somewhat disingenuous statement. Most gun homicides in the US are committed criminal-on-criminal, or criminal-on-victim. Very few are acts of "a crazy person", and even in those cases very few have ever been diagnosed with or presented psychotic symptoms prior to the commission of a gun-related homicide.
I therefore reject your guarantee that it would "actually make us safer". I also am pretty sure it would run afoul of ADA, and the 2nd Amendment, though that's a question for expensive lawyers.