Should scientists value philosophy?

Recently, when an interviewer asked the famous astrophysicist and science popularizer Neil deGrasse Tyson about his opinion on philosophy, Tyson replied that he has low regard for the entire discipline of philosophy. Tyson said that the problem with philosophy is that it bogs philosophers down in esoteric nitpicking over matters that will not affect anyone, whereas scientists like himself produce practical results in the real world. That is, Tyson dismissed philosophy as impractical. I think that is a rather common reaction from scientists about philosophy -- they dismiss philosophy as impractical. I find that odd, as people once recognized science as "natural philosophy" -- they thought that philosophy provided wisdom-lovers and knowledge-seekers with good ideas on how to collect data and analyze it for their own understanding. How did this philosophy-versus-science divide originate? When scientists dismiss philosophy as impractical, is this more the fault of the philosophers for being impractical or of the scientists for being too dismissive? How can philosophers explain the value of philosophy to scientists?