I think the reason is that we can make a neural network without having to have a person write the program. They are good at what they do because they have many many hours put into them that just wouldn't be possible to do with human beings. With all that effort and education, you have to make something that works well, even if the system is somewhat inefficient.

The downside is that you must have a large and decently recorded set of data to train with, otherwise you just can't make a neural network train itself with a relatively small amount of power.