The distance is needed only to calculate the Supergalactic Cartesian Coordinates or to convert between different Ecliptic Coordinates.

In all the other coordinate systems you are defining only the location of an object on the sky. In cartesian coordinates you are defining the location in space (x, y, and z -coordinates) so you must include the distance to accomplish that. For objects within our solar system the distance must be included in Ecliptic conversions because these distances are in the same magnitude with the distance between the Sun and the Earth and in some cases even with the distance between the Earth centre and the topocentric location. Therefore the distance is needed to avoid even drastic errors (think about an object lying between the Sun and the Earth!!).