It is a myth (at least in 2019)
A significant portion of homeless people do have jobs—they just cannot afford to pay rent. Some receive disability income due to physical or mental problems but still cannot afford rent. For those wanting to work—a common refrain among those interviewed by my research team—the complications of applying for a job with no address, no clean clothes, no place to shower, and the stigma of being homeless (or having a criminal record), make such individuals far less competitive in the low-wage job market.
(emphasis mine)
The 12 Biggest Myths about Homelessness in America by the New York University
Wikipedia hints that working does not prevent homelessness and some of the major causes of homelessness impact workers (sources are from 2001, 2004, 2005, 2008 and 2009):
- Lack of sufficient urban housing projects to provide safe, secure,
and affordable housing to the financially underprivileged.
Additionally for low wage workers rents can be unaffordable in areas
where their workplace is located.
- [...]
- Redevelopment and
gentrification activities instituted by cities across the country
through which low-income neighborhoods are declared blighted and
demolished to make way for projects that generate higher property
taxes and other revenue, creating a shortage of housing affordable to low-income working families, the elderly poor, and the disabled.
- [...]
(emphasis mine)
United States Conference of Mayors, "A Status Report on Hunger and Homelessness in America's Cities: a 27-city survey", December 2001.
"A Status Report on Hunger and Homelessness in America's Cities" (PDF). December 2005. pp. 63–64. Archived from the original (PDF) on December 30, 2008.
Vanneman, Reeve, "Main Causes of Homelessness" Archived August 22, 2009, at the Wayback Machine, University of Maryland
Cf. Levinson, Encyclopedia of Homelessness, article entry on Causes of Homelessness: Overview by Paul Koegel, pp. 50–58.
Center for Housing Policy: Paycheck to Paycheck Archived April 24, 2005, at the Wayback Machine
A quick note on Thomas Sovell. He writes primarily from a libertarian perspective, though he dislikes being labelled ideologically. His philosophy made him particularly influential to conservatives. In this article he is pushing a common wrong conservative doxa.