I worry about the things an investor-run shelter would try to make their investment profitable

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

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.