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?