And if you sell your car to some clown who later drives drunk and kills someone, the victim's family should be able to sue YOU for millions in damages, right???
Nope. Liability works best when it starts with the proximate cause of the harm, i.e., the driver, or, by analogy, the shooter.
Since guns like cars have the uniquely high potential to cause death to others, they both should carry similar liability insurance.
In order to operate a car, you need a minimum level of liability insurance. This lets the market - not government - play the primary role in determining who can drive or shoot a fire arm. And don't tell me that no limits can be placed on gun ownership, because prisoners are not allowed to possess weapons in their cell. There are plenty of instances where your right to use a gun is outweighed by other factors.
Listen son. Insurance companies weigh many factors when providing auto insurance. They consider age, driving history, etc. Same for owning a gun. The insurance companies could weigh medical history (mental illness), etc., before determining the correct cost for a given individual's insurance. And if you can't get insurance because you robbed one too many liquor stores at gunpoint, than your beef is with the market.