There was a time (ten to fifteen years ago) when it was legal to park your bike in between cars in Seattle. That was helpful.
In short, I don't think there are any significant Seattle-centric advantages to owning a motorcycle.
State law does not require mandatory insurance for motorcycles. I pay about $100/year for pretty comprehensive coverage anyway so the savings aren't that much (but I don't own a $20K Harley). Not unique to Seattle.
Motorcycles are faster in most types of traffic as they are smaller, more nimble, quicker and slightly less likely to create road rage driving competitions and challenges. I do things on a bike that I would not do in a car but nothing egregious. But not unique to Seattle.
You cannot lane split in Washington so that advantage is a non-factor. There are times when, if traffic is ridiculous, I will zoom ahead to see what the heck is going on. Ditto on unique.
Most bikes get at least 40MPG which is pretty good. However, older bikes probably put out more GHG emissions than a brand new Hummer. And the 2-stroke bikes and scooters are flat out eco-killers. Applies everywhere.
Parking isn't as Wild West as it was a decade ago but there are lots of places you can stick a bike that you can't stick a car where it is free to park and safe. Under the viaduct and at the ends of overpasses like the ones that come off of Capitol Hill and first hill into downtown. A little sketchy sometimes...
One of the biggest advantages is that if you get a parking ticket for not having one of those little slips you are supposed to stick on your headlight you can contest the ticket and so long as you are not there daily the judge will let you slide. Tell him you had one but it got stolen. It's a lie but I'll leave the ethical quandary up to the individual.
Parking in garages can be cheaper or even free. Some garages have gates that are not manned and lots of bikers just slip in and out of those. Some garages will charge a very low monthly rate for parking bikes- as little as $25/month. All on the up and up.
Of course having such excellent hospitals in Seattle is a big deal. Everybody eventually crashes. And if you don't make it, your organs will be that much fresher for donating to someone who needs them.
Compared to other parts of the world Seattle drivers are quite deferential to motorcyclists. Ever since I eschewed my leathers and cafe racer for a dual sport bike and Hi-Viz yellow/green road gear with orange helmet I have had virtually zero issue with drivers. If you've ever ridden a bike in California or New York/New Jersey you will understand how much better Seattle drivers are. And if you count Mexico or the Philippines than Seattle drivers are the epitome of grace and forbearance. Sure, there are the occasional knuckleheads and dumb-asses but I swear it feels like open season on bikers in parts of California at times.
The proposed registration fees like the ones defeated on the last initiative really pissed me off. I own several bikes because I am a hobbyist. To pay $80, $100, $120 for each bike is bullshit as I can only ride one at a fucking time. And that it cost the same as a car at all is also total bullshit. I voted for it anyway as I am a supporter to the things that the initiative was trying to accomplish but it pained me to do so.
In Seattle you can pretty much ride year round. That’s pretty awesome. So long as there is no ice I’m riding. There is heated riding gear available if you need some extra warmth.
Seattle has a decent motorcycle infrastructure. Nothing like Southern California but still OK. The Suzuki shop on Aurora is staffed by some good guys and the Moto Guzzi shop up the street is probably the best motorcycle dealer I’ve ever dealt with. The BMW dealer (Ride West) is good and Mick Valentine’s shop on Aurora can handle nearly anything German and English at a cheaper price. My experience with the Honda shop has not been particularly good and I’ve heard mixed things about Lynnwood Cycle (Kawasaki and Triumph et al). I hate 99% of all Harleys so don’t know anything about them or the local resources. There is also a good café racer scene here with some specialty shops staffed by reasonably knowledgeable fellows. Langlitz Leathers is all the way down in Portland but they are considered one of the best makers of leather gear in the world.
Well, I probably digressed into some points that were not exactly pertinent to your question, but if you have any follow up I’d be glad to try and help.