In an annual cruise season there are ten cruise lines and 18 ships that dock in Seattle from May-October. The business impacts of this industry are huge.
It is not just the cruise lines that will take a hit. The airlines that ferry people to Seattle, the hotels, the vendors that provide supplies to the ships and the associated tourist destinations in Seattle, Pike Place Market, the Space Needle, museums, shopping, etc., etc., will all see an economic downturn. This means the tax receipts flowing into the city's coffers will also drop significantly.
With some natural disasters there is a mini-disaster tourism bump that can come. Tour operators start operations so people can see the damages from the disaster. In this case, there won't be anyone coming to "see the coronavirus" and its aftermath.
At this point I don't see any upside to the economy of the region by being singled out as the birthplace of coronavirus in the United States.