If you worked in housing in Seattle you would know it's not really legal or practicable for landlords to exclude pets, considering the expansiveness of ESA designations. Almost every landlord already excludes pets outside of ESAs
There are numerous pet-friendly landlords, but typically the rent is not cheap. Pets have a real cost — they aren’t cheap for the owner, I don’t know why the owner assumes they don’t add cost to their living situation.
The main complaint seems to be that there is not a glut of cheap pet-friendly rentals, which is an unrealistic expectation in Seattle where the housing market is already extremely competitive.