Why is the insurance idea not a good one? Because it would require a change, not in insurance law, but in tort law, and not a fair one or one that gun owners should rightly accept.
We're required to carry insurance for our cars because there's a decent liklihood that we will commit torts against others -- actions for which we are legally liable. (We're not actually required to carry insurance, of course -- in many states, you can instead opt to just set aside a large amount of money to pay for possible damages, which only a very rich person would consider).
The reason making gun owners insure their guns doesn't make sense, then, is because gun owners aren't legally liable in the first place for the damage done with their guns -- and it makes little sense for them to be.
Of course, you might argue that that law should be changed so that if somebody has their gun _inadequately secured_ and it is stolen and used, then they have some fixed, capped liability. If that happened, then the insurance thing would take care of itself; people would buy liability insurance just as they do when they own something else (e.g. a house) that makes them liable. Mandated insurance law would only be required if it turned out (later) that people were frequently insolvent and unable to pay their gun liability fines. (Not that likely, in my opinion).
In other words, it is the liability law that would have to change, not the insurance law.
That said, I think the liability law change is a bad idea. To make it effective, the fine would have to be very large (hundreds of thousands of dollars at least), and that would create a terrible mental sense that the gun owner was somehow as responsible as the killer -- which is false, and would be met with legitimate outrage by gun owners.
Certainly a better compromise (say in the case of "assault rifles") than outright banning, but not a good one and not one that I would expect the anti-gun lobby to have the political capital to achieve. Admittedly an interesting idea though.