This quote from the third of these links suggests that the heavy coats of todays show dogs IS to do with show breeding. They'd hardly have been selecting hairy coats to improve working ability, since very very few were ever getting worked in the west.
"The first Afghan Hounds imported to Europe were mostly smooth coated with feathering that varied from sparse to heavy. The soft woolly coat grew through between the stiff hair, and at that time children on the street referred to them as “dogs in pyjamas” … no one would refer to them in that way anymore, as the original Afghan Hound coat p