The primary reason for owning a firearm is self-defense. Almost all privately owned firearms go to use in a non-aggressive fashion. Having a firearm is the perhaps the greatest deterrent to physical harm in all walks of life.
That being said, we can agree on the problem. There are those that will choose to use firearms to harm others who pose no harm to them or anyone they were enlisted to protect. It is this aggressive use of guns that must be deterred at great expense.
Although we can agree that that nasty outcomes of violent gun use, there are many flaws with your proposed solution. An armed civilian population serves as a better deterrent and better response than a government could ever hope to unveil. Even if the government accomplished the impossible task of disarming to population, at some date, over time guns would reappear in the United States, and without an armed populous we would be forced to rely on the government for protection services.
Let's pause for a second and think about how good of a job government does at protecting people today. When people call 911 they get a law enforcement agent. The officer's role on the scene is to investigate any crimes that may have taken place.
He may apprehend a suspect of a violent crime and transporting them to jail. Other encounters will entail ticketing someone - that is to say demanding them to appear in court for violating some law. But rarely, if ever, does an officer prevent violent crime from occurring in response to a 911 call.
Police patrols fail to prevent in a similar vein as response times would still be either still too slow or require a staff that no pension could ever uphold. There is, I'd imagine, critics that would point to the deterrent of violence created by the mere presence, or even existence, of such officers. But again the ability of the government to deter, even existentially, the threat of force they must interpose themselves so neatly into our lives that their no separation between their domain and our own - lest we leave some aspect of the individual's life unprotected after leaving them without their own defense.
The contrary solution - so I don't leave you empty handed - would be to allow anyone to procure whatever armament they so desire. In such a scenario we would bestow the responsibilities and capabilities to all in the country. Those that misuse their capabilities will be stripped of their freedom, to a measure deemed appropriate by Congress. There are still laws against murder, theft, rape, and all violent crime. The population could equip itself or enlist others in their defense. Such defensive products could be offered as cheap as the cost of such skilled labor demands, as seen in the bodyguard industry for example.
Either way, people will have the means to protect themselves in the fashion they deem most appropriate.
This thrifty yet thoughtful buying of protection cannot be met by government agents enforcing laws passed by politicians in Washington D.C.. Perhaps the connection between individual responsibility and entrepreneurial insight could produce a society armed and ready to fight all instances of tyranny, first here - and then across the globe.
We would extend the second amendment to the EU and rearm the citizens there. And so on...