Most of the homeless don't want to live somewhere cheap. They'd prefer to be homeless somewhere expensive. Unless you can force them to stay in the rural housing this plan won't work.

There was a survey (San Fransisco Homeless Count and Survey, 2022) which says 71% of the homeless in San Fransisco were living in San Fransisco at the time they became homeless, 24% were in another California county, and only 4% were out of state. But generally it makes sense that if a single county adopted housing first at a large scale these numbers might change. Additionally, the primary cause of homelessness is the severe housing shortage and the high cost of housing. So homes for the homeless should not be implemented in only cheap areas, but the expensive areas with the highest homelessness rates. This should be combined with a large increase in general housing production in these areas to mitigate the cause of the homelessness in the first place.