Let me make it easier to understand: "The U.S. is running out of places that people want to live."
We're realizing that living in an anonymous suburb on a tract of cheap land a 90 minute drive from where we work is stupid. It's terrible for the environment, it stunts social and business opportunities, and it is boring. More people in cities is good for the environment, good for economic equality, and good for sanity.
There are an infinite number of places that you "could" live, so your use of "running out of housing" is a straw man. By your definition, it's not even possible to "run out of housing".