Is it in any sense a useful order though? You can assign any order to any set of objects, but you'd want it to be useful. A hash - the more hash-ey it is, the less the order means AFAICS.
But it only needs to have this property for hashes of one particular size, whereas a hash map requires a function that behaves well for a variety of hash sizes. So there's an opportunity for using a cheaper hash function.