Well, a prop might prove itself to be purposive enough. And, that compels an artist to reuse it during the same shoot. Your eyes are not magnifying glasses that they can observe all the towel or fingerprint marks. So, you need to dry the items. Otherwise, such distortions are so visible, that the picture has to be captured again.
Rather than taking it as a burden, better read the following recommendations on how to keep the props clean.