It's not American guns that lead to our murder-by-gun rate; it's that we tend to frame problems in absolute ways, and go for the gun once we've boxed ourselves in. Americans have always seen themselves in terms of the individual against the world, and make our inspirational stories around uncompromising brave loners who aren't afraid to fight. It's built into so much of our popular entertainment, from westerns to spy movies to zombie apocalypses: the true man is the one who resolves his problems by terminating his opposition. Maybe it's part of the frontier legacy, where all men, decent or criminal, were beyond the shelter of the law, and everyone had to choose to fight or to bow down.

I don't think you're going to change this feature of American character by prohibiting items. It's based on something subtle and enduring. It doesn't grow from having guns in the house, or from watching violent movies, or from playing violent video games. The ideal of the fighting man is embedded in our history.