They are allowed on Interstates, frex on I90 from just outside of Issaquah to Spokane. It's not all that pleasant or fun, but they are allowed.
Shoulders suck as a place to ride though, it's where all the road debris hangs out, waiting to puncture a tire.
http://www.legislature.mi.gov/(S(disednjhhuuyovzmbvhdxfys))/...
Are you sure that Washington doesn't just have a provision in state law requiring action to close a shoulder?
Yes, that's why I said "(not limited access roads, just highways)", because of the ambiguity in the word "highway". A couple of states do allow bike access on a large portion of limited access highways, mostly in the west.
We don't have bike trails because they are expensive and little used (because of population density more than anything). That's a political reason, it isn't exactly a surprising or awful reason.
Unfortunately, even with wide shoulders and good visibility, "accidents" still happen thanks to unalert/hostile drivers (check out the recent terrible death of Mike Hall in Aussieland)
Rail trails are pretty cool to be honest, and there is a good and much needed network here. Of course, it will never be as extensive or well maintained as auto roads are here in the US for political reasons