Not the whole USA is armed, some states have bans on gun ownership and shockingly enough, those are the areas with the highest rates of violent crime. Chicago, DC, NYC come to mind.
If you ban guns and take gun ownership out of the hands of normal law abiding citizens, the only ones that will be armed are the criminals.
Criminals do not walk into a gun store and buy a gun and have it registered.
Yeah cos there are so many controls on state borders which don't let the guns from the states where it is allowed into the ones where it is not .... not like, say a FUCKING GREAT SEA and customs controls.