I lived in a housing market like that. It was a college town dominated by a church subsidized school. The students had to live in on-campus, off-campus and registered, or unregulated housing. The only people allowed to do unregulated housing were those who had their stuff together e.g. married or living with family. Housing was cheap and any landlord disagreements could be complained against the uni housing office. The uni provided so much housing that prices were based on the uni’s low cost instead of anything higher. A friend from high school had her dad choose to “invest” by buying a small apartment building out there, but even with his daughter as manager, he didn’t make a good return because he didn’t have the scale to provide the minimum level of service. I think he sold it.

Students there tended to get married and have children while still in school.

Long story short, housing market regulation can be done via a dominating entity over demand, but non market forces are not common everywhere.