There is nothing wrong with programs helping people out of homelessness (exploitative forced labor is no such thing).
Keep in mind that a lot of people getting out of homelessness can be really hard to achieve. Usually because of the involvement of multiple problems like drug abuse (alcohol whatever...) and psychological or other health issues.
These are individual, need proper treatment and sometimes there is nothing one can do about it.
For example in France and Germany there are institutions for long term alcoholics who have given up and are basically allowed to drink under supervision until they die.
They are provided housing, food, health care and (regulated) alcohol.
It sounds weird but is way more humane than having them living on the streets with all the issues this entails.
Is your private for-profit workhouse willing and able to properly provide for those people too?
https://www.ndr.de/nachrichten/hamburg/Trinken-im-Pflegeheim...
I think have a seen something similar from France i am sure similar institutions exists elsewhere too.
As i said drinking is supervised and from what i could gather that even keeps the most extreme excesses in check.
He's certainly mentally ill, but urinating in private place does not usually qualify as direct danger to the society, so no forced treatment can be applied.
What's next?
Very few mentally ill people realize they need help.
And every month or so hose it off for him.
The percentage of people who would actually continue to do so is small, but would be provided for. Anyone else in a similar house could just use the toilet.
I think OP was trying to get at the sad reality where severe mental illness is treated with some sort of loss in agency. You're still forcing some sort of solution they may not want and may work to sabotage.
You could advocate for encompassing services (e.g. regular visits from a nurse) but you'll quickly arrive at modern psychiatric facilities if for no other reason than scale and cost.