This is a very naive assertion. Providing homes reduces homelessness but many un-housed individuals will not accept the housing for a number of reasons to include mental illness or the stipulations required by the housing authority.

For a subset of the unhoused, yes. Some chronically unhoused people don't have the skills to function in housing, some chronically unhoused people have mental illnesses that make staying in housing difficult for them and the people around them. A small subset unhoused people want to live on the street. Homes without social services and a safety net is setting up the broad unhoused population up for failure, and then we wonder why housing programs don't work and throw money at something else.

Homelessness is an incredibly complicated issue. Mental healthcare is not the answer, medical care is not the answer, financial support is not the answer, housing is not the answer. Some combination of those things in the right proportion is the answer, and it's not one size fits all.