Exactly. The ACA made it so the homeless could get medical care without going broke. In my state, they’re mostly fully covered if they’ve bothered to apply for it.
However, most homeless organizations still push a “housing first” model because access to medical care doesn’t really make life on the street any better. In fact, being on the street leads to higher instances of needing emergency services. When people have a “home” to go to, you’ll less often needing to be treating them for frostbite in the middle of winter, for example.
A place to stay would drastically reduce the near-constant need for emergency services of this vulnerable population.