It's hard to believe that the problem is a lack of funds when the city's 2015-16 budget allocates $241m to help ~7k homeless people. It sounds more like we can't figure out how to deploy these resources effectively.
That sounds like a ton, but for the estimated 7k-10k homeless people in SF, that's $24k-34k per person annually. A lot of money, but not an insane amount given the high local costs of absolutely everything.
If things like the budget for those shelters and their employees also come out of the $241mil -- even assuming an even split -- you're probably looking at way less than $30k or even $20k per-person already... Assuming it 'only' cost $50 million to run it all, that's about $19k per person at 10,000 homeless, with 25k-at-7k.