I do think you're guilty of hyperbole here: "...long tradition in the United States of killing other people or oneself with a gun." Tradition? We may have more "gun violence" in this country but among responsibly armed Americans, it's not a tradition.
In contrast, "progressives" are just that. Give them an inch of gun control and they'll want another progressive inch, and then a foot, a yard, and a mile until they've totally gutted the 2nd Amendment and there is no private ownership of firearms in the United States. They think by doing so they'll make themselves more safe.
I think the reality is they'll just create an environment wherein the biggest, badest, MFers will, by virtue of their physical superiority and viciousness, establish themselves as the law and leader of the pack.
There is some truth to the old adage: God created man, but Sam Colt made them equal.