This is a non-sense that spreads because of North American style of housing. If you're talking about sprawling suburban houses then you're right. But big cities have provided reasonable housing for lots of workers for centuries. The only thing you need is to build more apartments in the cities that have an excess of job positions.
No, you can't just "build more apartments". For these new inhabitants you will need more grocery stores, more bus/subway stops and overall transportation, more hospitals, more firefighters, more restaurants, more gyms, more tennis courts, more of everything.
Of course. Big cities with all this infrastructure are nothing new. They existed in the past and are big in alive in Asia and other parts of the world. Only in North America we have this bizarre world where it seems like a strange thing to build cities and provide infrastructure for workers!
There is basically no large city outside of subsaharan African & maybe the subcontinent that has that development style and anything even approaching a sustainable 2.1 total fertility rate