As usual, there is a back story here which is not being reported. Low oxygen levels in the waters lead to not only algae blooms, but fish kill-offs, which affects both the tourism and fishing industries (two of our biggest industries)
It would seem to me that if they want to achieve better results, they should leave the dishwashers alone, and concentrate on the wastewater processing, but it may be that they are trying to reduce input from septic fields. A sizable chunk of Puget Sound (hood canal) has suffered from poorly maintained (or in some cases, non-existent) septic systems that discharge into the canal. When it was mostly small summer homes, it wasn't that big of a problem, but as more and more people have moved out there, it's been a real problem for local seafood industries. That's probably the drive behind this legislation - trying to avoid a similar problem in the San Juan Islands and Spokane River irrigation district.
Of course, a ban like this is ultimately silly, because people in these counties will just go to neighboring counties for dish powder, and when the state ban goes into effect, they'll stock up in Oregon. And with places like Victoria still discharging raw sewage into the Straits of Juan de Fuca, it seems like the sound has bigger fish to fry (if you'll pardon the pun)
But Puget Sound is many things: A series of essential maritime channels (most direct route to Asia!), a giant fishing site (Think Olympia oysters and Dungeness crabs, among other things), a tourism hotspot, and an ecological marvel. Because of this, it's the population center of an otherwise sparsely populated state. Trying to figure out a way for all of those interest groups to peacefully co-exist is almost impossible.