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!!).