Our homeless crisis is determined by factors unrelated to the amount of housing (though it used to be, and it’s important to build new housing in general) - nowadays we actually import homeless people to places like SF.
Basic supply and demand along with every study I've seen points to housing supply being one of and usually the main factor in the level of homelessness of a city.
As to San Francisco homeless coming from outside the Bay Area, that's true for only around 10% of the population. Most (70%) became homeless in San Francisco and many others became homeless in other parts of the Bay Area. See the `PLACE OF RESIDENCE` section from https://hsh.sfgov.org/wp-content/uploads/2020/01/2019HIRDRep...
As to San Francisco homeless coming from outside the Bay Area, that's true for only around 10% of the population. Most (70%) became homeless in San Francisco and many others became homeless in other parts of the Bay Area. See the `PLACE OF RESIDENCE` section from https://hsh.sfgov.org/wp-content/uploads/2020/01/2019HIRDRep...