The reason this worked is because 1) the charity took the time to do economic modelling that shows the actual benefit to government in dollars, and 2) the scenario is actually tractable to this sort of modelling.
There are a lot of nonprofits out there that can't get funding because their benefits are difficult to quantify, or because their benefits are too diffused and doesn't impact government bottom line directly.
Also they seemed to have avoided the corruption that is rampant in social services. My town tried something very similar to this, starting off with a new apartment building for the "chronically homeless" which very curiously was constructed at a per-square-foot cost about 4x market averages.
> After three years, researchers found that 75% of the Journey to Social Inclusion participants were still in stable housing, compared with 58% of the other group.
It's great to hear this turned into a win-win. A high rate of the homeless people in the program remained in stable housing after 3 years and modelling show that the program helps the government save money by investing in homeless people rather than dealing with them with police and medical services.
The return declines each year. See the section of the paper where they discuss how the two groups converge in outcomes as time passes.
(This is complicated by the high attrition in the control group: they lost track of a third to a half of the control group and so couldn't do an intent-to-treat analysis; they argue that the bias from this heavy attrition is probably in the direction of understating the benefits since it was mostly the ones who were worst-off at baseline who disappeared, but of course there's no way to be sure and one could easily argue the opposite.)
I'm not sure how you're coming up with "2.8% annually". This is an ongoing effort, not a one-time investment; the local government is spending money every year, and each year they estimate they're saving $1.32 for every dollar they spend.
There are a lot of nonprofits out there that can't get funding because their benefits are difficult to quantify, or because their benefits are too diffused and doesn't impact government bottom line directly.