I'm not sure I advocate for similarity between the requirements for a driver's license and simply owning a gun, but I'd like to see more stringent requirements for the equivalent to legally operating a car on the public roads. That is, for carry permits have more stringent training/competency requirements (many states require no "range time" at all).
Sure, I also think anyone who keeps a gun at home for self-defense is a fool if they don't regularly practice, but requiring certification in such training for simple possession of firearms would almost certainly require a constitutional change (since it's an enumerated right). An idea to consider, but not something that's going to happen any time soon.
I should point out that insurance won't cover any deliberate and/or illegal harm caused...no insurer covers illegal acts.
I'm not sure what you mean by "rapid fire." Do you mean fully automatic firearms ("machine guns" ? Those are already very strictly controlled. Do you mean anything but single-shot firearms? That would be a very extreme position, and not one I can ever see being implemented. I'd hazard a guess that 99.9999%+ of civilian firearms in the US are repeaters of one kind or another (semi-autos, revolvers, bolt-action, lever-action, slide-action, etc...).