There are 2 problems that I can see here that need to be tackled: shelter, and safety. It is _relatively_ easier to provide shelter: just 4 walls and a roof, basically. The more difficult part is the safety. City-run shelters are a haven for criminals, who are much better than the homeless in working 'the system'. And then there's the problem of amenities: showers, toilets, etc. Who will build them? Who will maintain them? And finally: homeless come with assorted mental/physical/drug issues. It's very rare to find a homeless person who does not have serious issues.
SF is doing a massive underground dig for a subway line. I often wonder: how difficult would it be to create some more room down there, and let the homeless just pitch a tent or crash for the night? But that would solve the shelter problem, which isn't that hard. It's the other facilities that are needed, which make the problem intractable.
Safety really isn't an intractable problem. There is absolutely no reason, apart from lack of money and will, that the city run homeless shelters have to be oversubscribed and unsafe. A few security guards keeping an eye out and throwing out anyone unruly, and better facilities with lockable single/family rooms would make them a far safer and a reliable option.
With a little bit of money, this problem of secure safe sheltered housing could be solved, even if all the other problems leading to homelessness could not. As you say there are often other issues leading to the lack of a stable life which cannot be easily solved.
Just as an example, we have sheltered housing round the corner from me in London for the homeless in a normal house - people have their own rooms, and it works, even if it doesn't solve their other issues. People seem to stay a few years then hopefully move on to a more stable life, I think that's the idea anyway. The provision here is inadequate as in the states, but it can be done with more money.
> A few security guards keeping an eye out and throwing out anyone unruly, ...
... and therein lies the problem. I know my evidence is anecdotal, but: there have been many cases here (in SF) of such security guards actually running protection rackets for drug dealers and participating in associated criminal activities.
Look: I know that if you throw _enough_ money on a problem, you can mostly solve it (or mitigate it). If we had $1MM to spend per homeless person, I'm sure we could put them up in top-notch places with full care. But then the ~7000 homeless people in SF would eat up the entire budget, leaving $0 for the rest of the city.
SF is doing a massive underground dig for a subway line. I often wonder: how difficult would it be to create some more room down there, and let the homeless just pitch a tent or crash for the night? But that would solve the shelter problem, which isn't that hard. It's the other facilities that are needed, which make the problem intractable.