Right now, Chicago has maybe 6 neighborhoods that people from outside of the city consider moving to. This puts a ton of pressure on the rents in those few neighborhoods and their surrounding areas.
But if the whole city had proper services, transportation, properly maintained housing units and relatively low crime, that should ease the demand on those few neighborhoods.
Instead, people just move into one area until it's too expensive to live there, then get pushed into another area until it's too expensive to live there, and so on and so forth.