In a sense, you're right, modern Philosophy doesn't have much immediate value; Philosophy has never even had tangible value, immediate or otherwise. The value that Philosophy has, and always has had, is in refining how we perceive--and thus subconsciously process--this strange realm we call reality. It's a subtle effect, but it's definitely there and quite pervasive. Take the study of ethics, for instance: I think we can agree that John Rawls is considerably more "modern" than most of Philosophy, but yet his arguments shed light on swath of ethical structures that had never been before categorized in such a way.
The fact is, philosophy is literally everywhere that there are living, thinking people: Politicians' worldviews dictate policy decisions. Mathematicians' worldviews direct and inspire new mathematical mechanisms. Scientists' worldviews drive paradigm shifts. Joe Nobody's worldview lets him eat pork and beans on a Friday night. There's nowhere you can go without running into it.
Our own cognitive abilities are far more malleable and prone to deception than it seems most people realize. The fruits of studying Philosophy, even if on the side, aren't found by merely understanding the arguments posited by philosophers, but in developing sane and contiguous perceptions of reality.