Utah has shown that housing people first alleviates a lot of stress. It takes away that fear of not having a basic, consistent place to sleep and be somewhat secure. Cities that implement housing first programs save a lot of money, as it's easier for those people to get to find work and get themselves out of the system.
Will some people abuse it and stay in government housing forever? Sure. But even with those people, municipalities still save money because a good chunk of the people can build their way out once their basic needs are met.