Well, even if such easy access was the problem, banning them wouldn't remove easy access to them, at least not for quite a while. You'd have to destroy 200 million privately owned firearms, then figure out how to keep police and military from 'misplacing' more weapons than they already do as black market prices outpaced improved accountability.
Regardless, I'm all for experimentation and were I Supreme Leader of the United States of America, it's something I'd try, for the sake of science...but probably after I'd introduce firearm use and maintenance classes into elementary schools, as correcting some of the astounding ignorance I see surrounding them seems like it would be both more practical to implement, and more effective at reducing the problems surrounding them.
Of course, with politics being the way they are, neither education nor controls are likely to move in any meaningful direction at more than a snails pace, and whatever reactionary changes that are pushed through in short order will be fundamentally flawed by the populist hysteria and ignorance behind them (the kind of legislature that implies a weapon's color or furniture somehow influences it's lethality, for example). And any experiments attempted will be compromised by poor controls, bias, and meddling for political gain.