Again, assuming the fallacy is common, why is it so common?
Think about the human auditory system (as described in, say, Wikipedia). It looks like the auditory system is just the set of things that enable a person to hear, e.g., the pinnas of the ears, the auditory canal, the bones of the middle ear, the cochlea, the hair cells, the auditory nerve, etc. If you take this picture seriously, then it is a small step to saying that one's hand cupped behind one's ear is part of one's auditory system.
If that is one's picture, then maybe the C-C fallacy isn't just a simple fallacy. Maybe it is that, when pressed on further examples, your view of systems leads to incorrect conclusions.