I have to agree with David that a rivalry with Washington ceased to exist a long time ago. As he illustrated Oregon has dominated the series to such an extent. You can't have a rivalry with a door mat. But, we can't just dismiss Washington, they will never be just a game on the schedule.
When the noise is too loud upstairs you can't ignore it, and it just gets worse if you ask them to turn it down, They tell you that they remember back when they stomped around with impunity and in their addled mind, that time still exists. But, you have found that if you toss an apple in the air he'll jump up in the air, catch it and be entertained for several hours.
Oregon would benefit with a true rival in the conference. USC's trajectory is similar to Washington's over the last 20 years or so, since Carroll. Stanford has academic prowess so they can't really be expected to compete, can they? WSU is the Poison Oak of the Pac-12. OSU is the little train that could, and Utah, who has been consistently good since joining the conference.
Now I have to get some more apples.