If this was as you claim, then an entire nation or larger region would not have to chip in to pay for a program of a small city.
That small city would just simply balance its own books and ledgers - since they are saving 100K with a 20K investment!
http://www.endhomelessness.org/pages/cost_of_homelessness http://usich.gov/usich_resources/research_and_evaluation/cos... http://www.politifact.com/truth-o-meter/statements/2012/mar/...
The biggest costs are pretty concrete. They are 'after the fact' emergency services like emergency room hospital care (vs cheaper preventative care) and jail (instead of housing). It's clear that these costs are higher for the homeless than average, but that leaves the question of housing changing that for this specific group of people (e.g. maybe they are just inherently more likely to end up in an emergency room) which is a valid question.
The evidence is that people with housing are more able to get the help they need earlier (such as preventative care), and are less likely to commit crimes out of desperation, because they have housing. This leads to a much lower rate of using these expensive services, leading to a clearly lower cost to provide housing vs concrete cost of emergency services.
That's why I believe this approach is both humane and effective. This is why I believe housing first is better for everyone.
What I haven't yet seen is evidence of the impact on society at large.
What is the impact on society, and those who have worked hard for their housing, financially and psychologically? While it may make financial sense, humans are emotional creatures very sensitive to perceived fairness. In the ultimatum game, people refuse 'unfair' offers to their own detriment. [0]
Do the number of people on these services grow or shrink over time? Free housing enhances the welfare trap[1], where people may be better off not working. It is not a silver bullet and needs to be paired with appropriate policy to be effective.
Britain reduced their welfare trap by raising the first tax bracket, fired half a million government employees, and now has their highest employment rate in history.[2]
[0]http://en.wikipedia.org/wiki/Ultimatum_game#Experimental_res... [1]http://en.wikipedia.org/wiki/Welfare_trap [2]http://www.spectator.co.uk/features/9475222/the-coalitions-j...