Required liability insurance isn't a practical means forward for either side. If all gun owners had to buy liability insurance, it would be inexpensive enough that everyone could afford it and it would make no difference. It is illegal to insure criminal or unlawful activity -- that is the crux of the efforts in some states to ban "concealed carry insurance." Because insurance companies would never be on the hook to pay a dime for the illegal use of guns in crimes, their actual exposure would be extremely low and they could not justify high premiums. Indeed, we already have lots of insurers offering "concealed carry insurance" that in some cases might actually pay for the legal defense of criminal acts. This insurance is voluntary, and so it has very few people paying the premiums. Yet it's often quite affordable.
Before the state could require the purchase of liability insurance for firearms, it would need to clarify the grey area here. Are these pre-paid legal services? Or are they insurance for criminal acts? If insuring criminal acts was ruled out, the insurance company would be on the hook for what is essentially the prepaid legal defense of criminal acts, which is not something the State is going to sponsor. So then what are they insuring? Firearm accidents? Is that really the plague the state is trying to resolve? Whatever little liability for lawful acts that insurers would have to cover, without having to pay for legal services, and having so many premium payers, the premiums, compared to existing concealed carry insurance, would be a pittance.
I'm certainly not suggesting anyone capitulate to the demands for liability insurance. It's certainly an unlawful infringement. My point is that it would not financially burden gun owners or actually pay anything to victims of crimes because insuring criminal acts is unlawful. So these efforts are a waste of time.
The people who've engendered these gun control schemes would be better off focusing their effort on reducing the incidence of hoplophobia, and working toward reinforcing good behavior with guns. If people aren't afraid of guns, hateful aggressors are less likely to perceive them as an effective means to strike terror into our society. If more people model good behavior with guns, not only will incidence of hoplophobia be reduced, but the relatively small portion of people that are fascinated and obsessed with guns that are at risk for expressing themselves in a destructive way, will be more likely to find productive and positive ways to pursue their passion.