Many states have adopted stand your ground laws that protect shooters in public spaces that accidently(with or without negligence) either unintended bystanders or innocent persons who are wrongly believed to be a threat. This is the most uncontroversial situation where insurance should be required. These innocent people need to be protected and many of them are not insured themselves.
As this blog has argued people who have permits to carry weapons into streets and outside the home. These people are more likely to confront real and perceived threats with an audience of bystanders. They represent an additional risk over those who only have guns for protection in their homes. These risks and the relative ease of insuring against it are described in another post “Enacting a Concealed Carry Insurance Mandate”