The "controlled borders" between the US and its neighbors are each more than a thousand miles across, and I'm led to believe that most of those in favor of gun control are sour on the effectiveness of securing them with a wall or other such measures.

Moreover, contraband flows toward the places where it's prohibited. If certain firearms went from not prohibited to prohibited then they would flow in rather than out.

And I'm not saying a national ban would have no effect, only that it would have a similar effect to a state-level ban -- regular people would follow the law, and then you might get e.g. fewer firearms suicides (but more non-firearms suicides). But if you expect gangs to stop arming themselves because of "borders" or national law, just look at Mexico.

The demand would drop and so would gun manufacturing. There would be less guns on the street and more effective securing/training of legal guns/owners.

Clearly there is a spectrum of choices that can be made, some more effective than others. As mentioned, state borders have effectively zero restriction in movement and should be taken in context with any criticism of local gun laws.

Why would there be less guns on the street? Aren't the vast majority of those illegally obtained anyways? IMO the more likely response would be that all the guns that were previously stolen/criminally obtained legal guns would become fully automatic since there's no reason not to at that point. (Manufacturing cost difference is basically nil, and if you're already smuggling an illegal rifle might as well make it automatic)

Guns aren't exactly rocket science to make, and the plans are available online. Good guns, reliable guns, safe guns? Not so much, but why would the criminals in question care?