You forget the target market for the Shuffle, people who want a ludicrously tiny player -- for whom the nano is excessively large... They like to work out while their player is clipped some random place, and they don't want to go looking for the buttons if they want to change tracks or whatever.
The corded controls make a lot of sense for this segment -- buttons on the unit as well would probably have been way to tiny to use, most likely.
Really what they should have done was just put inline remote support in a chassis like they had, but they were obviously feeling some pressure from somewhere to make it tinier.