'Strict liability' is the appropriate legal standard for ‘inherently dangerous’ items. Under 'strict liability,' gun owners would be responsible for harm caused by their firearms regardless of negligence or fault, regardless of who pulled the trigger.
Requiring proof of insurance while possessing a firearm would make enforcement easier. Allowing confiscation of uninsured guns would get illegal guns off the street.
This approach avoids Second Amendment issues by not requiring government registration of guns or gun owners. Insurers would set standards and premiums for those seeking firearm liability insurance.