If a city has 1 million jobs but only homes for 800k workers, then you will always have 200k workers who are priced out of homes. Or if you do it the communist way and assign homes with arbitrary price ceilings, you still have 200k people without homes although now it is the 200k most recent immigrants and not the 200k poorest, but the problem is still there.

So what do you suggest we do about that except build more homes?