Yes, you’re missing something: Much of the funding goes into prevention. SF only directly spends about $3K per homeless person. There are a lot more people staying housed because of those funds.

While I'm certain SF could be doing a much better job with their existing budget, that's not a very meaningful statistic. You'd need to know how many more people would be homeless in the counterfactual scenario where they weren't spending that money.

For what it's worth, that's way less than (less than half) the amortized yearly cost of a California prison inmate: about $70,000.

https://lao.ca.gov/policyareas/cj/6_cj_inmatecost

That is the average cost? How much would that be if we looked only at the min-sec cost?

If it is anything like the institutional system, the people who need dedicated watchers 24/7 are so, so much more expensive that person like my family member, who needs only occasional help managing his normal life and doesn't need anybody to guard him.

At a single moment in time there are about 7500 homeless people in SF, but about 20,000 are homeless at some point during the last year.