I'm not sure that the outcome of analysing arguments is always that no one is any wiser concerning the issue at stake. And that's because there are several possible results of such analysis, all of which would seem to help us better understand the issue at stake and the justifiability of possible answers: (1) Perhaps the (implicit or not) argument the person offers for her answer is invalid; in that case, the philosopher is able to show that, whether or not her answer is right, her argument doesn't give us reason to accept that answer as right. (2) Perhaps there are assumptions the person makes in offering her answer but that she doesn't defend; in that case, particularly if the assumptions seem questionable/controversial themselves, the philosopher is able to show that the answer requires more defense than the person has offered. Or (3), perhaps the way the person has framed the question closes off certain possible avenues of thinking about the issue; in that case, the philosopher is able to point out...

I'm not sure whether this is "generally acknowledged" (or whether it counts as "solving a problem") but I think the following might be an example: In explaining human action, many people are quite tempted by what has come to be called 'psychological egoism': the view that each person has but one ultimate aim in acting, namely her own welfare (or self-interest). On this view, there is no such thing as genuinely altruistic action--action aiming ultimately at another's welfare--but only ever action that, at best, appears altruistic but is really ultimately self-interested. But in his Fifteen Sermons (1st ed., 1726), Joseph Butler (a philosopher and Anglican bishop) showed fairly decisively that this sort of view cannot be right. For more, see Part 1 of the the Stanford Encyclopedia article "Egoism": http://plato.stanford.edu/entries/egoism/