I worry about the things an investor-run shelter would try to make their investment profitable
Giving money to your local homeless shelter encourages homeless people to move near you (see San Francisco). Making a lot of risky investments in businesses encourages people to start new businesses. One of these has positive second order effects on economic growth.
Those kinds of stats typically consider people like couchsurfers to be "homeless", which is not what normal people typically consider "homeless".
are there stats which suggest "couchsurfer" and non "couchsurfer" homeless people have significantly different origins?
Neither helps homelessness. Building more affordable homes is the solution. Which also has 2nd order effects.
People that need help are going to where the help is, shocking /s
i understand your true and noble motivation, but the law of incentives is an iron law, and it tells us your subsidy will incentivize the burgeoning industry that demands more shelters
They often enable people their way to recovery. Individuals are better off because of them. Do you have a source for your claim that more shelters cause more use of shelters which is what I think you’re saying right?