>> negligent homicide (although it's usually treated as manslaughter instead of murder)
Not usually. It can never be treated as murder. If it was negligent then the killing lacked indent per se.
>> If you are unable, or unwilling, to handle a loaded weapon with the requisite amount of care to avoid negligence
Good luck selling that to the AARP. People have medical incidents behind the wheel every day. A heart attack/stroke/seizure can easily result in a crash, including deaths. We don't lock people up for that unless they were negligent, unless they had some reason to know it would happen. Everyone one of us may suffer an aortic dissection or brain aneurysm at any moment. That's why large commercial aircraft have two pilots. Driving while human is not negligence.
That said, many car crashes are probably caused by negligent actions anyways. Someone who is speeding through a stop sign without stopping is negligent in doing so, especially because the kind of people who do that once tend to do it all the time.
When you drive at speed (above ~25-30 mph for someone not protected by a giant steel cocoon, I think ~50 mph for someone who is), you are now in control of a loaded weapon that will kill or seriously injure anyone against whom it goes off. If you are unable, or unwilling, to handle a loaded weapon with the requisite amount of care to avoid negligence, then perhaps you are not deserving of the privilege of handling that weapon.