There is a middle way here. Currently-active fields in philosophy sometimes (usually?) lack bounded questions and precise answers, yet are not silly (ethics, for example.)

I don't think philosophy is about finding answers, the discussion itself is its purpose. Consequently, there is always the risk of generating closed, self-referential discussions in which the subject of the discourse is the discourse itself (post-structuralism vs. structuralism?) It also seems to be an accepted practice to hang an elaborate argument on nothing more than a personal opinion, as if doing so turned that opinion into an objective fact (I am thinking specifically of some of the arguments over consciousness.) For these reasons, I think you have to pick and choose from the offerings of philosophy if your goal is to teach general thinking skills.