Coffee cup patina; is there any logic in not washing the cup I first encountered the practice of never washing a coffee cup, when I was sternly warned, and nearly physically threatened by a former employer to never wash his coffee cup. 

Apparently it is an old military tradition to never wash out your coffee cup, and being a retired service man he continued the practice.

Is there any logic behind this, does it noticeably effect the coffee, or is this just an old, superstitious tradition?
It may be superstition but many people, myself included, don't wash out their coffee cups. I rinse out my cup but don't wash it - I don't want soap going into my favorite coffee cup. I like the way it smells of coffee. I don't have to see or touch my favorite coffee or tea cup to know which one is which. 

In addition I never use soap on either my coffee or tea filters.

Would I notice the difference if I had two identical mugs - one with the "patina" and one without? Maybe not. But I prefer it that way.