In the free market they will leave and get replaced. Or enough will leave and wages will go up

But they can commute in like many people do, right?

Yes, to an extent. Commuting adds friction to working there, and if it becomes too much of a burden then people are likely to relocate.

And in this specific case (head chef at a popular bar) living in the neighborhood allows him to keep abreast of other bars, local trends, etc which benefits his work.