Stopping guns right now in America doesn't = criminals have no guns, that's silly. There's an entire black market for guns, there's millions of guns lying around in American homes, so many that the government wouldn't be able to track down and get or even attempt to spend the money doing so. Criminals who wanted a gun could get a gun without much issue regardless of if it's legal or not.
You know what banning guns would do? It would create an even bigger black market and an even bigger demand for them (from criminals and gun enthusiasts alike), and instead of being sold in stores, they would be sold on the streets (they already are, but far more so).
Your solution solves nothing and just makes it where people who like guns for legitimate reasons don't have legal access to them.
I dont say get rid of guns. Firing ranges, police situations etc. Hunting or whatever. But a gun for protection? You know how many gang members have bought their gun and claim it's for "protection"? Most guns are registered down the line. Trace your guns, you'll cut out a huge percentage.