It definitely doesn't do any good other from a hatching/fertility point of view other than make them look nicer.
Washing removes the protective cuticle covering on the egg which keeps out bacteria, even dry cleaning them will remove it.
Washing would be a very last resort for me, I won't say i've never done it but I don't do it very often.
I'd just stick them in as they are, as you said, the hen doesn't wash them
But yeah, I have had some manky hatching eggs through the post!
get some fresh bedding and nesting material down folks!