The fact is, there is a correlation between more guns and more shootings while bans don't correlate to reduced shootings. These parameters are difficult to reconcile. I think the best role for gov't in this case is to provide free training to registrants and require the training.
I would not suggest bans, I suggest education and I also suggest a more responsible discourse from gun advocates. While bans are not the answer, an increased number of untrained gun owners certainly contributes to the problem. If the training is good and employs veterans, why would anyone refuse to avail themselves of it? I can't imagine why even the most hardline gun nut would complain about such a requirement. I think they would gladly send their kids.