You don't need to subsidize, Palo Alto. You need to Build. More. Housing.
Yes, this. Subsidizing makes things better for the lucky few who happen to be at the top of the list for subsidies, but does nothing to address the root cause of the problem. Municipal zoning regulations serve to limit the amount of housing that can be built, and this limit falls farther behind the demand with every passing year.
Let me play devil's advocate here. Having lived in the Bay Area for about five years, I can testify to what a desirable place it is to live. Climate, geography, the city, everything. Coastal California in general might in fact be literally the best place in the world to live. If you could wave a magic wand and make the median house be $250k, and then went to every person in the US and asked if they'd move there, you'd probably find something like 50% of the population would, in fact, want to move to coastal California if housing prices were $250k. There are currently 30 million people in California, and I'm guessing most live in coastal California. And then you'd have 150 million people that want to move in.
If you built more houses to lower the price, people would simply move in until house prices were bid back up to $800k in San Francisco (where they are now). But the only difference is that you'd have, say, twice as many people, and quality of life for everyone would be worse. So building more and more houses to lower prices only works if you can build enough to accommodate all the people who want to live there and not lower the quality of life too much, which I'm not sure you can do in coastal California. It might end up like all the people in L.A. that thought you could fix all the traffic problems by just building more freeways. Didn't work out so well. You just ended up with a maze of freeways, all of which were just as crammed as before.
I don't know what the solution is, though. I'd love to move back to SF sometime, but housing prices are just comically high.