As I understand it (and as my friend who is an SF police officer where 90% of his job is dealing with the homeless), the much larger problem is SF's (& perhaps society in general's) failure to provide institutionalized care for people with severe mental disabilities.
No amount of money, support systems, or opportunity for getting off the street is going to help people with severe schizophrenia or dementia who have no family or safety net. A lot of these people the only solution is for them to be institutionalized. Unfortunately, there isn't much of a way for someone to be institutionalized against their will (unless they are causing danger of harm to themselves or others) so they continue to live on the streets.
I think what this city really needs is a place to send people deemed in need of institutionalizing, and the ability for that to be determined. Of course that would never fly in a place like SF, but I think it would be a happier life for those people than life on the streets.