Yungerman: That’s one of the reasons I don’t think that P’shat is the only reason for it, though I’m sure it plays some part of it. It makes too much sense not to.
Nechomah: I don’t think the point is that the nails are Tamei (and just to use proper terms, we’re not quite talking about Tumah here). I think the point is that whenever you remove something from your body there is a Ruach Ra’ah that rests on your hands that must be removed. Besides, I have a feeling (can’t source it though) that this Ruach Ra’ah only comes when you actually intentionally cut all (or most) of your nails. We don’t see anywhere where you would have to wash your hands after pulling off a hanging nail or plucking out one hair (or when you get a cut; you have to wash your hands after bloodletting/giving blood).