I did a very nice researched blog post on how to solve homelessness in SF and then decided not to publish it. The problem is that I'm very analytical and logical about solutions to social problems and most people, including the internet mobs, are not. It's very difficult to convince people that what they are doing in the short term is actually disastrous when the thing they are doing satisfies an emotional need they have now. The best we can do is make arguments that shift the burden of responsibility from one civic agency to another.
To answer homelessness, we need to understand the responsibilities of our civic institutions, the limits of their theoretical jurisdictions and the underlying causes of homelessness. Ultimately, your view on who is responsible stems from your understanding of the purpose of different forms of government. My views start from a strict constitutionalist point and then evolve as various judicial outcomes have moved the goalposts.