Do cities have the power to make sure of such a thing? It's not like the mayor can just go around setting prices and wages to the level she thinks is best.
Public housing generally does not come with a nice enough environment that teachers and plumbers will agree to live there. Maybe there’s some way to build public housing which doesn’t come with drugs and petty crime, but if there is I don’t think American cities know how to do it. The conventional wisdom is that the right way to do affordable housing is distributing it evenly among all the new complexes in the city.