While true I don't think this driving problem is used as an example for something you should use ML for rather an example to show how you could apply it.
Nevertheless, it is impossible to say why a 'neural network' would be better than some other model function with a large number of parameters. It's true, there are some significant successes achieved with NNs, but there is not a lot of work separating necessities from contingencies. Basically, a lot of it is trial and error.