How do you even begin to discriminate on that? The USA lacks a residency system like other countries.
I agree with your point, but it’s not possible to implement here, which is why the non profits continue the conflation.
That covers the large majority of homeless that SF should target for help and are all easily accessible to the city government. You can imagine corner cases (attended a private school, lived in SF but worked outside it) but it'd be an improvement over the status quo. Even many of the corner cases could be captured with additional documentation that would require a bit more effort on the applicant's side.
I believe you would find that this is illegal. Shapiro (Shapiro v. Thompson, 394 U.S. 618 (1969)) and its progeny address this issue on point.
(I feel obliged to mention I believe your number because of your expertise, simply because of the number of people in this thread who failed to say that).
Sure. But the approach to dealing with that subset of people should be different than the approach for the subset who were once employed and renting in San Francisco and then ended up homeless through a health emergency, job loss, or eviction. The latter group has shown the ability to sustain themselves in SF in the past, while the former hasn't. And, morally, the place of original residence is responsible for them, not the taxpayers of San Francisco.
If nothing else, people with longstanding ties to the community and economy should get preference for services compared those who didn't. And homelessness advocates get this: the entire point of conflating them is to increase sympathy for the people who just turn up.