It's worth noting that Seattle and DC have vastly different representations on their boards. In DC this is two representatives picked by the governments of DC, VA, MD, and the feds each, and in some cases not even appointed by elected officials. In Seattle, this is a board consisting almost entirely of elected officials of counties and municipalities.

Seattle's method works because the responsibility of elected officials is quite clear and their voting records are transparent, whereas a diffuse chain of responsibility via appointment is not.