I don't know.
But given the killings per capita vs. every other western country, it's clear the US is in no shape to handle guns in a loose fashion.
I'm too lazy to link to gun killing/violence charts (edit: just did a few links), but I wouldn't be surprised if the US per capita violence is more than all other developed western countries combined. I've seen those types of charts and the US is off the charts. Every other first world country has pretty similar/muted rates, and then you see the US in the number one spot and it's like the chart just morphed into Mt Everest.
And we're talking on a per capita basis, not absolute numbers (which the US destroys as well), since the US has 300,000,000+ million. So based on pure math, it makes sense the US has more absolute number, but not at the huge over and above numbers they get.
It looks so odd, you'd think the computer calculating the numbers has a formula error.
Mental disorder checks should be done, but IMO not as important as it seems. There's lots of smart maniacs out there. The stereotype of a maniac is he's some dummy. But in reality, many are intelligent and can surely game any personality test. This Vegas shooter was an accountant. So right off the bat, it's pretty certain he's pretty smart and clever already.
And when it comes to approving the process, who knows how loosey goosey the approval process is.
http://www.cnn.com/2017/10/03/americas/us-gun-statistics/index.html
http://www.bbc.com/news/world-us-canada-41488081