I would even agree with urban relocation if one city had a disproportionate number of people trapped in inter-generational poverty and another had extra jobs. I don't think "deep cuts" to urban welfare are ever the solution. I do think that the welfare system should prioritize setting its recipients up for success.
This equation isn't typically true for urban areas, so there's no reason for people to move. (See Detroit for details on exceptions.)
There just aren't any houses, so their quality of life takes a greater hit than staying put in the form of huge commutes and dramatically increased cost of living. See service workers or teachers in San Francisco.
1. https://www.curbed.com/2017/6/20/15834514/rent-transportatio...
2. https://www.technologyreview.com/s/607957/the-unaffordable-u...
3. http://www.sfexaminer.com/mayor-lee-spend-44-million-sf-teac...
A basic house is $65k in Morgantown: https://www.zillow.com/homes/for_sale/Morgantown-WV/22898744...
And a nice house with a 10 minute funicular commute to Downtown Pittsburgh (the Paris of Appalachia) isn't too much more: https://www.zillow.com/homes/for_sale/11363350_zpid/globalre...
And one can pay much less if one wishes: https://www.zillow.com/homedetails/2040-Lowrie-St-Pittsburgh...
Scarcity-driven housing costs are one of the biggest problems in a few coastal cities— but in much of the country, the problem is poverty.
Both Pittsburgh and Morgantown are pretty prosperous, yet remain affordable enough for blue-collar workers to own homes close enough to the center of the city to commute by foot, bus, streetcar, funicular, PRT pod, or bike. The neighborhoods I posted are a bit rundown, but perfectly livable— I'd live in any of them.
The schools aren't necessarily great in the Pittsburgh neighborhoods but they usually aren't in rural Appalachia either.
I don't disagree that moving is hard when one is poor and one relies on one's social connections for a lot of support. It's just not because of a lack of houses in the prosperous parts of Appalachia.
Housing shortages on the coasts are a huge issue, and a huge issue for national inequality— but overbuilding and inner-city abandonment remain a bigger issue in a lot of cities in the middle of the country.
Additionally, there are other cities that have more opportunity than closed mining towns do. At the bare minimum the people need to relocate to someplace marginally better with ANY economic opportunity, because where they're at now has NO opportunity, not necessarily some place that is the top of economic opportunity.
For people on the low end of the earning spectrum, the lack of tangible benefits for moving outside of a vague promise of better job prospects makes staying put a viable option. If you worked at McDonalds, would you move across the country and away from your entire social support system for a chance to commute two hours on public transit to work at Arbys? I wouldn't.