There would be NO government support of any kind. That way, religious people would have a real live cause to work on and the "homeless" would be dispersed and not gather at bus stations, skid row, etc. The homeless could repay the church/temple by doing odd jobs, mowing the lawn, washing windows, litter pick-up, etc, while getting training for jobs, getting detoxified and prepared to enter the mainstream.
Those who chose to opt out of the program would be on their own to survive as best they could, knowing that the option of joining the program was always there.
I personally believe that much of what we see is because the church abdicated their responsibility a long time ago in favor of letting the government take care of the poor.
In essence, my church does something similar to what you suggested. But we only have the folks with us two weeks out of the year. The other 50 weeks, they’re at other churches. And they can only stay in the program a certain number of weeks, then they have to be out on their own. We provide food, shelter, showers, laundry, career counseling, haircuts and more. We also provide food for a “soup kitchen” once a week downtown.
Not because we’re anything special, but because we believe that, as part of the Body of Christ, this is one of the things we should be doing. (and our ministries don’t stop there. These are the ones I’ve been directly involved with)