Because full depends on infrastructure. Tokyo sits at ~37.5 million people demonstrating few cities are near any real limits. https://en.m.wikipedia.org/wiki/Greater_Tokyo_Area

Cities in the United States have no mechanism to prevent nonresidents from moving in. If nonresidents want to move in and capacity is not expanding it will drive up prices and result in economic pressures on the poorest residents until they vacate enough space to reach an equilibrium. A city can control how many people get to live there, or it can work to ensure that all current residents can continue to live there, but the Takings Clause of the Constitution essentially prevents doing both. Saying "sorry, we are full" (like San Francisco) amounts to telling a large portion of your poorest residents to get out (like San Francisco). People are generally pretty bad at putting two and two together and realizing that their misfortune is the result of poor capacity planning by their city government, but they still tend to get angry and angry people tend to vote out whoever is currently running their city, so pissing off a large swath of residents is rarely a good strategy.

Well, that does happen implicitly, except the full statement is "Sorry, we are full to our limit of low income residents." They eventually get replaced by richer residents.

Because here in the United States that isn’t something that you can say.