It's not "move to a rich area". It's "move to an area with good opportunities for production (roughly 'good jobs', although self-employment is also a possibilit

It's not "move to a rich area". It's "move to an area with good opportunities for production (roughly 'good jobs', although self-employment is also a possibility of course)". That's a very different problem. An area with high cost of living, almost by definition, has a lower margin of production and thus lower real incomes for such, adjusting for productivity.