This is non-economical thinking. If a city becomes too expensive for service workers, service workers will leave the city, lowering supply and increasing wages. Its a non-problem from an economic standpoint.
An example I can think of is that Monaco (tiny but wealthy city state) is serviced by mainly French and Italian citizens who drive 2 hours per day for higher wages in Monaco, so it does seem like it works. The downside is that this creates a lot of traffic during rush hour.
