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)
https://www.nyu.edu/about/news-publications/news/2019/september/HomelessQandA.html