This short treatise was written by Galen in the 2nd century AD. Although it's about the relationship between Philosophy and Medicine, I feel that it offers a good way of answering the question "Why bother studying philosophy in the first place?"

Even if studying philosophy never results in any tangible progress in answering the big picture questions, it will still sharpen your reasoning skills. And proficiency in what Galen names "The three parts of philosophy: ethics, logic, and science" is essential to being an educated, well rounded person.