It can be easier to set up and maintain than hand-rolled solutions. Best example I can think of is speech recognition - previous systems used hidden markov models, gaussian mixtures, triphones, and all sorts of complex and obscure things that had to be tuned by experts. Now they just use an end-to-end neural network that goes directly from sound to letters (almost anyway; I believe the input is still MFCCs).

I agree it's not magic but it neither are 'manual' methods and at least the maths is a lot simpler.