A better way to frame the spending is, how many additional people would be homeless if not for the efforts of San Francisco. There aren't just 6,700 people that refuse to be helped but tens of thousands on the cusp of a very bad situation.
I'd wager approximately 0. If you mean, how many additional people are homeless in San Francisco because of the efforts here, then the number surely isn't negligible but the wealthiest area in the country seems like a decent place to extend a little humanity. What's the alternative? Treat our homeless like shit so other people don't want to move here?
At that rate they could, you know, provide homes for them and feed them? Sounds like that's part of the plan (500 units), but not in a way that makes sense to me.
Micro-apartments at ~200sq.ft., with really basic (read: mostly plastic/easy to wash, plus maybe a cot) furniture, could go for ~$800/month and still be a good deal for a developer. That's $9600/year. Throw in inexpensive food at another $800/month, and it would be $19,200/year, or a savings of $14,800 per year. Partner with a developer, guarantee the rents, and let the private sector fork over the capital for the building of WAY more than 500 units.
A lot of the cost is actually far more than $34k/person, by the way. There are charities that leverage this fact by finding chronic emergency-room users and getting them a home, food, and sometimes a companion animal. [1] When a homeless person checked into a hospital can cost $9000. An emergency room visit can cost $3700. [2] When someone has serious health issues, they can visit the emergency room multiple times a month; some end up costing the taxpayer $44,400 per year.
Apparently 90% of the homeless at any one time are just going through a bad spot in their lives. And giving someone a place to live can break the cycle of homelessness: You need to have an address to get a job, typically. You also need to be able to shower. Let them keep living in the cheap apartment if they want, but if their income passes a threshold then they need to start contributing to the room & board.
Or don't force them to pay; food and shelter really should be human rights anyway. Why not start in San Francisco? Everyone else would benefit by there being fewer people peeing on walls or sleeping on sidewalks, and by the (relatively) cheaper labor pool that would be available.
Go one better. Provide them all of those things, as well as /a/ job (not necessarily one they're trained in) as well as time for and inclusion at, training for jobs that are open.
I imagine that maintenance of public infrastructure is a thing which won't go away any time soon.
If you define the above as a poverty line (and the re-education time slot is also usable for personal crafts/recreation/etc) then you've also very nicely defined a minimum wage which must be beaten. Providing the apartments at a monetary level in areas also defines a value level for housing in a given area, which is one way of eliminating price gouging (or at least giving added value when it is done).
Not a bad thought, though some of that 10% of the homeless who are chronically homeless probably should be allowed to just fail to go to their job with no consequences.
Ideally they'd have social services and/or psychiatric care, and some of them, after sufficient care might then be able to work. But some are just going to be chronically unemployable.