I can't say that owning a firearm should mandate having the insurance, but personally I immediately purchased an umbrella insurance policy from Geico. The policy was for $1M and cost $85/year, but at the same time I was able to lower my auto insurance premiums $40/6 months so the policy only net cost me $5/year. Seemed well worth it. The umbrella policy isn't a policy specifically about firearms. It covers all of your actions, whether you accidently ended a life of an outstanding high earning citizen because your lawn mower kicked a rock and hit them just perfectly on their temple, or because you defended your life in your home with a firearm. The policy only covers legal acts, so a defensive shooting has to go your way in the courts if charges are brought. On year two I bumped my coverage to $2M for around $35 more/year. Geico can provide coverage up to $5M, but they won't go over $2M without a review to understand why you'd need so much. The minimum policy was $1M.
If someone has alternate options I'm interested. The idea of a shooting club getting a group policy is an interesting one as well. I'll have to mention that one next time I'm there.