I can see two pretty big distinctions and I'll try to be civil. For starters, you have a constitutional right to bear arms and don't have a constitutional right to drive a car. So it's going to be hard for a federal laws putting such an encumbrance on the exercise of the right to bear arms to pass constitutional muster. (At least in Deezestan, a state law would be fine.)
If you want to make it constitutional then put the insurance premium on ammunition for the gun.
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I'm certain someone can account for presence of ammo or not in insurance premiums. I know you are aware, that "right to bear arms" translation you are using now is not the version the SCOTUS held until the 1970's. That was when the NRA effectively changed our legal view for that to be an absolute right, unencumbered by rules, and diminished the clause "well regulated militia" which is in the same sentence as the right to bear arms. I'm not even arguing over removing guns though...just forcing gun owners to be more responsible.
Second, why do we impose liability insurance requirements on drivers? You're right about the policy argument, but that logic could be applied to all sorts of situations in which we don't require liability insurance. There are reasons why we require it specifically of drivers. It's because driving is ubiquitous, so if we didn't, it would have massive, systemic consequences. Countless innocent people would be getting massively hosed every day. Furthermore, the probability of damage-inducing accidents is very high. In fact, they are routine.
We put that insurance requirement on drivers when cars became ubiquitous and the damage they did when used carelessly became an issue for the other drivers. As of right now
per Americangunfact.com 38% of Americans over the age of 18 have a gun and the US has 393M guns in the marketplace. Compare that with
only 276M registered automobiles. Yes, we have >100M more guns that cars in homes. With Open Carry and expanded concealed carry laws the guns are even more prevelant. They are now outside of the homes. Guns are the most common murder weapon (by magnitudes), the most common suicide option and accidental deaths.
This site has unverified (by me) information on accidental gun accidents. I'm saying, that the US fascination with gun ownership has now crossed that same divide that we did with cars where the volume of them results in more injuries by their users so those users should be financially liable for the responsibility they choose to bear.
This isn't generally true of gun owners. I'll admit that I don't know the numbers, but I'm willing to bet that a far greater percentage of cars are involved in potential tort liability than guns. It's just a lot easier to get in a car wreck than to screw up with a gun.
Above are some numbers. We can argue about where the threshold should be but I'm saying we've past it and with the open carry laws we KNOW gun accidents (and violence) will be more pervasive so it's time to get ahead of it.
No, I don't think forcing gun owners to have insurance will cure gun violence any more than liability insurance for cars has forced all those who refuse to get the insurance to stop driving. Anything that forces a would be gun owner to recognize the awesome power of the gun in their possession and treat it responsibly is a good thing, IMHO.
For those who care, I own 2 guns, a handgun and a shotgun primarily for personal protection in the home. Both are in a gunsafe in my bedroom and I'd be willing to pay
additional insurance for the responsibility of owning them.