This article is a good overview of the research about treatment-first vs housing-first approaches. The last paragraph is pretty clear on the real difficulty: >The major obstacles to resolving homelessness remain ideological. It is politically hard to sell the idea that people who take drugs or are disruptive should get free housing – even when the evidence shows that is actually what works.
I guarantee I could produce a program that would be acceptable to conservatives and provide free housing. Note also that Utah, a very conservative state, solves homelessness in exactly this way. It just might be that the housing would not be provided by funneling huge amounts of tax dollars to the rentier class, and might involve constructing more houses, and therefore would be opposed by the left.
That's trivial; prison. (Ignoring the part where prisons now charge prisoners rent...)
Finding a solution everybody can agree on is much harder than finding a solution only one side or the other can agree with.