Of course they're not solving the root of the problem. The issue of homelessness is not caused by a lack of homes.
Granted, there are homeless people who have a stable life but work a job that just doesn't pay enough to afford a home, or people who are between jobs and are temporarily homeless. But those people generally sleep in a car, cause few problems, are largely invisible, have most of their needs met in some way, and are generally not the people we are concerned about when talking about "the homeless".
The Homeless™ usually have more complex issues like untreated psychological issues, drug problems, etc. And while the previous group would rejoice about small cheap housing, it does little to solve the issues of The Homeless™.
https://www.oecd.org/content/dam/oecd/en/data/datasets/affor...