Here's the thing, we have fixed homelessness in the US before. The sort of homelessness we see today is the result of two policies: the elimination of public spending on public housing, and deinstitutionalization of the mentally ill. Both of these were done for (some) good reasons; conditions in both could be horrendous, and mental institutions were absolutely horrid. But they were also done for ideological reasons, and the resources to house people in their communities were never provided. Public spending just stopped, and local and state governments were left to jury-rig solutions.

The other aspect is that the State of RI has literally developed a plan to end homelessness. Everyone in the system absolutely knows how to end homelessness, what's required is political will to procure the funding to do it. It's not a question of capitalism, it's a question of action.