This is a slippery slippery slope. We've yet to find a way to stop trouble through proactive prevention. We don't (except for tom cruise) put people in jail based on the likelihood of them committing future crimes and our foundations are built on the idea that until you screw up you get the benefit of the doubt. Guns are never going to leave our culture. We fucking love them. We are a warrior/militaristic culture and get everything we have now through the liberal use of firearms.
We can tighten up on ownership though. Background checks are a hot button issue for no reason. Some people are already restricted from gun ownership but in states like Florida they just buy a gun out of the newspaper. No tracking, checking nothing. A couple hundred bucks and you get a gun. If the gun owners would come up with make sense laws and support them, much of this debate would go away.