Well, note that I'm not advocating abandoning all restrictions...the fact that we require a simple criminal background check (done electronically, usually only taking a few minutes to complete) is precisely what makes our system work so well--criminals can't pass the check, and thus can't buy firearms through legal channels. Because of that, the incidence of legally-purchased firearms being used to commit crimes is quite low (it does happen, often in domestic disputes).
I am saying that further restrictions on law-abiding citizens will not have any effect on the incidence of guns being used to commit crimes, because the criminals are already getting their weapons through underground channels.