The 1950's brought us the idea of nuclear cars Styles. Fallout 3 just capitalized on it. The HIghway man in Fallout 2 was a single vehicle there is no basis for it being a model for all cars. That being said the microfusion batteries exploding could be causing the radiation. The old FO2 style cells did have the radiation sticker on them.
They were still batteries and the car had an electirc engine. Bethesda did not need to come up with Nuclear Powered cars because Fallout already had microfusion electric cars. The very fact that the cars in Fallout 3 explode proves how very stupid the idea of a car with a nuclear reactor in it is.
You are driving you're nuclear powered car. You crash into a car infront of you. You die in a nuclear fire ball, which causes the cars around you to blow up, and that causes all the cars around them to blow up. Before you know it every car on the highway is blowing up, killing hundreds if not thousands of people. It will not stop until there are no more cars around to blow up. LA would have been nuked to hell by one careless driver getting into an accident, because of the famous traffic snarls its known for.
Then there is also the insain logic in giving anyone with the cash, their own nuclear bomb on wheels. Wouldn't need to stock up on fertilizer and get a rental truck anymore. Just go out an buy you're own nuclear weapon on wheels.
It would have been fine to say they had nuclear reactors. Totally stupid to say they blow up when shot at.