"What problem is that? "
The culture of violence.
"Assuming you think certain people shouldn't have guns, how would you propose keeping guns out of the hands of those who shouldn't buy them, other than conducting a background check at the time of purchase? "
Well first i would look at how they get their guns, actually that has already been done. Because only a tiny percentage would ever come close to being affected i would throw out the idea that UBCs are even worth considering as the numbers prove they are not worth it.
So then i would be left with the actual problem and figuring out a solution. I am already far ahead of those thinking that pretending like UBCs would do anything are.
So as we are already light-years ahead of the UBC crowd it would be about addressing things like gang violence, mental issues and education. That way there is at least a chance of doing something.
But the worst and dumbest thing we could do is think that the people who are already getting their guns through illegal sources that would not be affected will magically decide now to comply with the law. All that is is a an emotional placebo with no effect.