Here's how I read your question.

1. Many machine learning techniques work, but in ways we don't really understand.
2. If (1), I shouldn't study machine learning

I agree with (1). Could you explain (2)? Is it that you would want to use neural networks etc. to gain insight about other concrete problems, and question their usefulness as a tool in that regard? Is it that you would not like to use a magical back box as part of a production system?

EDIT I'm using "machine learning" here to mean the sort of fuzzy blackbox techniques that don't have easy interpretations, not techniques like logistic regression where it is clearer what they do