Not having it both way is an argument to fairness. You should want fairness in a game of checkers. It was never a thing in employment anyway nor will it be.

A high local real estate price is a reason you can't profitably work for less and its something you can profitably express to an employer if they will take it into account in order to access the local labor market.

A lower local real estate cost is a reason you could work for less not a reason you ought to want to.

You absolutely should try to have it both ways to the greatest extent possible because they are too.