Gun safety needs to be treated similar to automobile safety, with required liability insurance.
Just like an automobile can cause damage to others' lives and property, so can a gun. Since we require every automobile owner to carry liability insurance, the same requirement should hold for gun ownership.
The involvement of the insurance industry brings natural market driven regulation to gun ownership. For example, more dangerous guns would require higher insurance premiums, and the owners' safety background would affect the rate.
The natural free-market driven regulation of the insurance industry minimizes the amount of regulation the government needs to impose, thereby eliminating the need for an extended government bureaucracy.