I think there bigger reasons at bay for why WA is able to sustain free income tax.
Look at it from a sociological perspective. The population of WA is on par with that of Arizona, both are within 6 million. Arizona's income tax rests at 2.x-4.x%. Yet as a desert state, I'd imagine AZ needs more resource management than WA does; pure logic without any backing in this statement. Examples like the interstate freeway, water preservation and conservation and such. WA probably doesn't need much of that due to the plethora of natural resources.
Look at surrounding states with a low income tax rate (say ~5% or under) and you can discern that ones with smaller populations AND with a few or no major metropolitan areas (Seattle, Las Vegas, or Wyoming State, etc) like Nevada, Wyoming, South Dakota they generally have low population, low or nonexistent tax rate.
Although, we have to take into account WA does have some kind of taxable earnings on businesses however, so it's not exactly scoot free. But that probably really applies to Seattle and Spokane, but Spokane is like, only a half of seattle.
My thinking is that population size, attractions (depending on what), federal uses within the state (highways, bridges, etc), city life all play a role in this.