No, you just make people have a requirement to carry gun insurance. See if the insurance company wants to write you a policy unless it’s sure you’re storing the gun properly. Maybe you need to provide a receipt for a storage locker before they will write the policy.
Maybe you do have to have someone inspect it. Plenty of states have motor vehicle inspections.
Let the free market solve this problem. Right now. Gun owners want all the toys they can dream of but want zero responsibility for when someone inevitably uses their gun to murder someone.