LOL, this is one of my favorite flavors of rants you hear from people calling for gun control, the one where they call for all the laws that we already have that didn't work. A doctor already has to report a dangerous patient and anyone adjudicated as insane is not allowed to buy a legal gun and anyone convicted of domestic violence or a felony has a lifetime legal gun ban.
None of these type of things work because they only impact the 99.9997% of gun owners who don't commit gun crimes, not the 1 in 10,000 people who is a habitual gun criminal.

The background check is a joke, nothing happens if you fail so if you have ill intent then you can go buy a gun on the black market. What is the point?