We pretty much do let anyone behind the wheel of a car. Once you earn a license, it can only be removed for cause in most states. One is not difficult to get, unless you have very significant visual or mental impairment that examinations can identify. We let people drive at a younger age than we permit them to own property.
We do this because it's difficult, bordering on impossible, to function without a car in much of America. The right's argument is that a gun is just as fundamental a need. Just like with driving, what we find empirically is that as state regulation of licensure and behavior decreases, fatalities and injuries increase.
Like you, I would prefer to see more regulation of these activities, rather than less. If you don't have a gun, and I don't have a gun, we can't shoot one another or ourselves. The right's fears that someone else might illegally possess a gun are not unfounded, but even the Old West heavily regulated firearm possession. Most everyone owned a gun, but in many places people were expected to check it with the sheriff when entering town, and pick it back up when they left.
A libertarian approach like Haley's to an issue where there is a clear and demonstrable externality is both short-sighted and selfish. There's a hundred years of theory and results that prove her wrong.
