And I agree that, once upon a time, philosophy did give birth to the sciences (once called natural philosophy), which have obvious utility. Philosophy these days doesn't produce any scientific research though. The sciences, once they developed into mature branches of thought, left philosophy. Questions like "what is X" in the Socratic sense don't have any place in science. We do teach scientists the scientific method, and perhaps they get a basic smattering of Popper, learn the name Ockham, and so forth, but that's it.
And is this ignorance of philosophy a good thing or an argument against the importance of philosophy? There is more to the philosophy of science than positivism and Karl Popper you know. Maybe they should be learning Kuhn? Lakatos? Feyerabend? Most science students will never hear these names, which is a shame given that these were all professional philosophers who believed in the importance of the scientific enterprise and had some extremely important things to say about how it should be done.
It's also true that any claim has epistemological or metaphysical implications, but these are either trivial or better relegated to the sciences. We don't need much philosophy in either case--and the questions for which we might need philosophy seem faintly ridiculous once one tracks them down.
Trivial: I know this computer exists because I'm sitting here typing at it.
Better relegated to the sciences: How do my senses interact with the world to get me this information?
Philosophical: But what if you were in some experience machine, or subject to an evil demon-god, who made you experience everything just as you do, except there actually isn't any computer or anything else?
This is an obvious caricature of philosophy more reminiscent of first year undergraduate introductions to the nature of the philosophical enterprise than any serious contemporary thinker or line of inquiry.
Then there is moral philosophy, or ethics, which I agree is useful, but much of moral philosophy doesn't ask substantive ethical questions, but is concerned with very abstruse meta-ethical questions of distant relation to our actual concerns about actions and values.
Um, what? Peter Singer? Hannah Arendt? Untold other contemporary academics in universities all over the world? Aren't war, the holocaust, abortion or euthanasia substantive issues with an ethical dimension? Besides which, the "abstruse meta-ethical questions" which other thinkers are dealing with provide the frameworks and debates that other philosophers which deal with contemporary issues are drawing on for their own studies. All disciplines have divisions of labour with people working at various levels of abstraction, and everything from the tiny painstaking empirical groundwork through to the metatheoretical work at the highest levels of abstraction is necessary for a healthy discipline. For example: I read Deleuze (a continental philosopher of the highest level of abstraction) so that I can rework aspects of Bourdieu (a "mid range" sociological theorist who also did empirical work on class processes in education amongst other things) in order to understand elements of the experience of homelessness in contemporary young people (a pressing social issue with obvious "real world" implications).
Ultimately you're not arguing against philosophy per se, you're arguing against a caricature of philosophy and its institutionalisation as a separate discipline in universities. With regards to the institutionalisation issue, at a certain level of abstraction disciplinary boundaries become arbitrary (the line between sociology, anthropology, and political science comes to mind here). But each institutionalised discipline reflects a distinct and fruitful, living tradition of inquiry. Philosophers deal with certain questions in certain ways, and nobody else does exactly what they do. No, they are not chemists or physicists or political scientists, but that's fine because they're dealing with questions that none of the members of those disciplines are able to contribute to.
But really, philosophy doesn't need to have some kind of instrumental reason for existing. The fact that you don't think it's useful, or that contemporary philosophers don't get cited in economics papers or government reports, is irrelevant. Getting rid of contexts in which critical thought for its own sake is valued and encouraged can only be bad for society.
ps: You've forgotten social theory, political philosophy, analytical philosophy, and philosophy of mind to name a few.