Scientists do not need philosophers to tell them what questions remain unanswered. On the contrary, whatever field of study it is, e.g. (say) Big Bang cosmology, the scientists who are researching in that field generally know infinitely more than the average philosopher about every aspect of current (or past ... or planned future) research in that field, and they are usually in a vastly better informed position to know about all sorts of questions that would not even be apparent to philosophers and others who are not directly involved in the research.
If the main (or only?) role of philosophy is now reduced to the claim of “asking questions”, then that is really no longer a valid basis for using taxpayers money to keep running degree courses or university research qualifications in philosophy.
Really what has happened is the slow realisation, from Galileo onwards, that science has made most of philosophy redundant. At one time (e.g., roughly pre. Galileo) philosophy was claiming to explain the world around us. And at the time it seemed to be the only option (apart from religious belief of course). But science has changed all that. Quite simply – philosophy has proved almost useless at discovering and properly explaining the world around us. Whereas science has turned out to be phenomenally successful at it,... to a level waaay beyond anyone's wildest dreams/imagination.
If you want to spend your life engaging people in endless arguments about the meaning of words from a dictionary, then philosophy is an excellent way to do that. But if you actually want to understand the world around us, then the only known way is through science (and it's turned out amazingly good at it!).