I think the main difficulty with site is that it's designed to gather multiple geometries (areas, lines, points). So if it's supported then we should also make sure that it's indicated what its different parts actually stand for. The same applies to public_transport and street. In case of boundary and route we keep only the main geometry, respectively area or line, but for these other more complex relation types this probably wouldn't work as well.

As for this list of relation types from imposm mapping, I think it needs some general revision. route_master doesn't seem to be really supported yet (possibly the mapping can be amended somehow to make it actually work). Others in this list, namely restriction, destination_sign, enforcement and connectivity, seem just useless as almost no relation of these types has wikidata tag.