If deep learning is a black box, then why are companies still investing in it?
Easy answer: utility.
The strength and applicability of "black box" NNs has been regularly validated in the past few years, and business is concerned with results. (i.e. they don't care how the sausage is made, so long as it gets made.)
I think that the universal approximation theorem plays a large role in why companies and governments are investing in deep learning, it states that theoretically an ann can approximate any continuous function with n-dimension input variables. Specifically it states that feed forward nets with a single hidden layer can do this lending credence to the implication that rnns and cnns are also capable of universal function approximation. So they are investing because they have continuous functions that need to be approximated and really the best tool for the job is neural networks.