usa – Why must hotel customers check out after a stay longer than a rather low number of days in the United States?

This appears to be related to the COVID eviction moratorium:

(I)t is critical to protect tenants and residents of traditional dwellings from homelessness, as well as those who have lawfully occupied or resided in less traditional dwelling situations for 14 days or more, whether or not documented in a lease, including but not limited to roommates who share a home; long-term care facilities; transient housing in hotels and motels; “Airbnbs”; motor homes; RVs; and camping areas …

As to why this measure was taken in Seattle but not in California, I can only speculate. Seattle has experienced a higher-than-average level of homelessness over the past several years, in no small part due to soaring real estate prices. It may be that a significant number of people in Seattle rely on cheap hotel/motel stays for temporary shelter when they lose their homes (due to rent increases, eviction, condo conversions, etc.), and it was felt that evicting such people would be bad for public health. But again, this is just speculation on my part.

It appears that in “normal” times in Washington State, the line between “transient accommodations” such as hotels and actual full-on rentals (with the additional protections so implied) is 30 days, not 14. See WACS 246-360-001, which defines transient accommodations as any facility offering stays to guests for less than 30 days.