One big limitation is RCW 84.52.050 (Limitation of levies) which I think implements the 1% constitutional max allowed levy. I read somewhere that Seattle is at a levy of about 9.4, so that would be a hard limit right there.
>...If total citywide property value drops by 50%, the tax rate would hit its legal maximum ceiling, and the city would have to make up the money somewhere else or cut spending.
And the city wouldn't even get all of the increase it is allowed as there are other tax districts who would also want a higher rate. The tax increase that would be allowed would be prorated with the other tax districts.
(The 1% revenue growth cap you referred to earlier is a different statute and a different issue.)