The concept of responsability does not work if somebody is mentally ill. Each individual can cause much more damage than he can pay, e.g. as a gunman. Especially guns have a terrible cost-to-damage ratio.
A voluntary solution could include to make the manufacturer liable for all damages caused by his product. Car manufacturers and car dealers world be asked to check their buyer's driving background. Gun manufacturers would be asked to check their buyer's mental background. This instrument of third-party responsability would impose uncalculable costs on manufacturers and dealers, so that manufacturers obviously prefer a government solution.
Car manufacturers could add a breathalyzer that prevents drunk driving. However, a mandatory breathalyzer would make a car more expensive. Some people would refuse to buy a car with breathalyzer, they would destroy the breathalyzer, which cannot be punished if the non-aggression principle is exercised in a strict way. In the long run, it would be cheaper for the society to send drunk driver into a state-operated prison than to pay for private devices which are more expensive.
In some rare cases, voluntary solutions may be cheaper, but in most cases, governments have proven to be the cheapest solution.