Let's say that this program actually solves the problem of homelessness for the mentally ill and drug abusers who dominate the hard core of those permanently without shelter at a reasonable cost. Currently the program is funded by a mishmash of public and private funding sources.
The problem with public funding is threefold. Political pressures to cut spending may yield across the board cuts that hamstring a program. Isolating a working charitable institution from such pressures is a positive step. But even with stable funding enshrined into law, it is neither right, nor just to force people who may be on the brink of homelessness themselves to pay for such an effort. But worst of all, public funding brings along with it a restriction on the obligations you can require of participants in the program. I can easily see how the ACLU might bring a lawsuit that a rent paying publicly funded housing unit cannot lock out its residents as the Ohio program does.
A superior solution would be to establish a fund that would invest and out of the profits of those investments pay for these housing units and the staff required to keep them properly running. Those who would seed this fund would know their own finances and could afford their contributions. Societal generosity would create the conditions for a decent program to continue without having to worry about political support and the legal limitations that public funding sometimes brings would be eliminated.
Update:
I should have posted my source material, Dean's World