One tidbit here: A subsidy to the employee is a backdoor subsidy to the employer. Income based programs that pay relatively low income individuals to remain in high(er) cost areas (housing subsidies for example) allow employers to keep their wages low. In fact, they provide an incentive to do so with income and work requirements that are necessarily tied to these programs. Subsidizing standards of living in areas with rising costs of living through welfare programs create a perverse incentive within the labor market.
This does a real number on local economies in multiple ways. Primarily, it expands wealth inequality as it allows those with more resources to continue to pay the same “low” prices for goods that should cost more as a result of the wage inflation that would be occurring in the area IF labor prices were to rise in response to the reduction in low skilled labor available, after being driven out by rising rents.
Treating the entire country or even state as one large pool of resources leads to the problem you outline succinctly. Very narrow bands of the economy (metro areas) don’t react to changing input costs because those costs are being covered by other regions through wealth transfers.