I take issue with framing homeowners as "those with power", particularly when talking about SF. Most people in SF are renters, not homeowners, and could easily overpower any self interested NIMBY homeowners... But they don't, for various reasons, but one of them is that they don't care either.

Aside from housing, a lot of homeless people are in need of mental healthcare, and that's something no particular city is equipped to deal with without backing from the state.