I think the point of the empirical arbiter is an interesting one. My second paragraph can indeed be used as an argument for the absence of one in philosophy.
But where is such an arbiter in science? After all, science is inductive, not deductive. It can give you lots of good reasons and evidence to believe a theory, but the principle of falsifiability requires that a counterexample must plausibly exist.
If either philosophical or scientific experiments were to reach an unfalsifiable conclusion, I think we would have a serious problem on our hands.
One consequence is that philosophical experiments rarely reach a conclusion (except when science does catch up, as will probably happen over consciousness, for example.) I have come to realize that reaching a conclusion is not the point; the discussion is the point.