But only if it were convenient.
I think it is quite obvious to anyone who read it, that rp point is about accessibility to weaponry, not criminality. Not having guns is not going to make those with a criminal bent suddenly law-abiding. But if one takes away the means, it will make them less effective/lethal. The harder you make it for one to obtain something, the less that something is to acquire.
40% of the gun market is "unregulated." That is, conducted without background checks. It doesn't take a leap of logic to realize that those inclined to cloak their activities in secrecy will gravitate in that direction. Eliminate that market, and it becomes more difficult to hide. Require universal registration, it becomes more difficult. Limit number of purchases, more difficult still. The more roadblocks, the harder it becomes. The harder, the more expensive. Slowly, the beast is starved.
Even if you triple the rate of application denials, the vast majority - 95% - of transactions would still go through, hardly affecting law-abiding applicants. For the criminal class, however, obtaining those weapons would become significantly more difficult. And for he rest of us, the streets concomitantly safer.