Problem is, anywhere you go, you'll run into the local NIMBYs.
Or let's say San Francisco actually subsidizes some town out in Central Valley, I dunno, Hughson for the sake of argument, buys up loads of farm land adjacent to the town and turns it into a much nicer place to live because those dollars will go further, puts in some groceries, parks, a whole community basically. You've now turned Hughson into a much nicer town, and it will attract more people wanting to live there, and you're still subsidizing a whole other city in the process increasing the cost of living. Not to mention moving our entire homeless population there would effectively double the size of Hughson straining local resources and utilities, so probably a lawsuit and more money to subsidize it further.
So now you've done all of that, but since this is Hughson, there's no jobs except farm work, and the locals probably have that covered so now they need good transportation to the nearest decently large city (Modesto and Turlock) to find some jobs. Now that you've got this satellite city, how does it sustain itself? Because at some point, San Francisco taxpayers are going to start asking themselves, why are we subsidizing Hughson? Assuming you got them to agree to it in the first place (which you won't). City charter amendment hits the ballot, it probably passes, but the wording is so poor it has negative knock-on effects for all the other land the city owns outside of the county line (the Airport and Hetch Hetchy mainly), Hughson and Stanislaus County are left holding the bag on a largely unproductive neighborhood that is a drain on the local coffers and almost completely dependent on subsidies from people richer than them.
I'm sure by this point they'll be real excited about bulldozing some houses to make way for some bullet trains they were previously gung-ho about stopping at all costs, and depending on the legal status of the property left behind, they can either seize them because nobody is paying property taxes, or seize them with eminent domain and put them towards some new productive purpose that once again, leaves these formerly homeless people homeless.
This is still better than the alternatives: hoping the State of California steps in to do something about it (they won't because nobody in California likes San Francisco except people who live in San Francisco), or hoping the Feds step in (they won't because hating San Francisco and hoping it falls into the ocean is a national past time, as American as liking Baseball).
tl;dr we spend money trying to "solve" the "problem" locally despite the high cost of living because San Francisco only has San Francisco to depend on. Anybody in power that claims to like San Francisco doesn't actually like San Francisco, they just love our money.