Look, the "you can't tell me exactly how it would work down to the last detail and not have any failures or we're not doing it at all" mentality isn't going to fly here. How would it be enforced? The same way the current ones are enforced; ATF would spearhead and maybe create a new subdivision directed specifically towards firearms. Are there issues currently? Sure; let's at least hold them to the same efficiency standards as the private sector, though.
As for how it will cause a decrease in illegal gun ownership, the point is to make it harder to get guns period. Less guns in the country = less access points to get them illegally.
Think about it - do you really think widespread use of guns is going to make this a safer country? If everyone in Detroit had a gun, it would be a far worse place than it is now. If nobody had guns you'd see a decrease in total killings but probably not violent outbursts and attacks in general. Neither of those are possible or probable, so let's try to cut a middleground. We want the least amount of total guns, and we want to make sure that the guns that are there go to the most responsible people and the people who need it the most. How do we make sure of that? Background checks, gun registrations, stricter carry requirements, use your imagination.
I don't get why you're playing so hard and fast on this - why is it on those who want stricter gun control laws and restrictions enacted to prove why it would reduce guns and not on you to prove why more guns is going to make us safer? The evidence is pretty clear cut: look at gun-related deaths in Australia before and after the Port Arthur Massacre, and then look at the laws enacted in response to it and how widespread firearms were in the country before/after. Then look at something like Columbine, Sandy Hook, etc.
Australia reacted to a massacre with restrictive measures and as a result have less gun ownership and less gun violence. We react to massacres the complete opposite way and what do we get? More massacres, more frequently. We can't go a week without a mass shooting in this country. There was a website up for a while called
www.LastMassShooting.com that kept track, and it never got over like 20. That's INSANE. I do not understand how anyone can look at data like these and not come to the conclusion that gun violence is directly linked to the amount of guns present. Are there extenuating circumstances? Sure - there always are. But that in no way, shape, or form means that we should abandon all hope of reducing firearm violence through legislation. It works, period. Show me another place where lax gun laws led to less shootings; I promise you that there are far more where tighter gun laws led to less, and I think we should be basing our legislation of proven methods and empirical data, not the whim and fancy of personal interpretations of a 200+ year old document written before something like a semi-automatic handgun was a thing.