So... You don't need a license to own or drive a car on your own property, I don't think. Or go through a background check to buy one.
It's just that we have public roads, upon which it's difficult to hide a car while in use. Yet routinely many people drive unregistered and uninsured vehicles.
Not to mention in many cases, you can carry a gun in public, and you do need a license that has to be renewed, just like a driver's license. So the original poster's point is moot.