I totally agree with you about the need for better drivers' training, especially in the United States. Quite frankly, my "driving exam" was a joke - a 5 minute drive around the courthouse square (again, I lived in a small town - cows outnumbered people where I grew up). Fortunately, my parents spent a lot of time teaching me how to handle the responsibility of driving a car.
Driving is a responsibility, just like owning a firearm or having root on all your company's servers. With great power comes great responsibility.
However, many of the items the parent mentioned, short of having an accident, are not even concerns for me and I would classify as minor inconveniences. Running out of gas is a minor inconvenience. A flat tire is a minor inconvenience (assuming you know how to change a flat, and even more minor if you don't). The others, again short of an accident, are things that are not likely to happen assuming you are aware of your surroundings. Don't park where you aren't supposed to. Don't leave valuables in plain sight - pretty much the same precautions you would take on public transit to avoid becoming a victim of crime.
I don't want to seem as though I'm opposed to public transit. I think it's great where it works and, if it were an option where I lived, I would probably use it when it made sense to. I was thinking about this last night and I've noticed I tend to use it more on the west coast than on the east coast. I actually like TriMet in Portland, and I've used Caltrain, VTA and BART when I'm in the Bay Area with little to no issues. But I would probably avoid the subway in NYC again and MARTA in Atlanta was one of the more terrifying experiences I've ever had as far as feeling unsafe.
The thing is, a large percentage of the population of the US lives in areas that have no public transit at all. Articles heralding the death of the car (like the link) tend to focus on cities, and suburban areas near them, that have adequate public transit while completely ignoring the remaining segments of the population that live in areas where public transit is not, and probably never will be, a viable option. For these areas there are simply no other options other than cars.