It works for single family homes, but it breaks down when you start talking about multi-tenant facilities.
There are far fewer single family homes on the market and they are a lot harder to bring up in the market. However, multi-tenant facilities cost a lot less to bring to market but there are few owners of those buildings.
With a much smaller set of unit owners, it makes collusion a lot easier to pull off. Only a few facilities need to participate in order to raise the prices and once it goes up for the large owners the smaller owners will happily raise their prices because "it's competitive with market rates".
The part that's totally divorced is that the cost of these units has nothing to do with business expenses and everything to do with market availability. A new player can't really come in and disrupt things and even if one or a few actors start undercutting the others it doesn't matter because they only have so many units they can sell which will fill up quickly.
The whole thing has driven up housing prices to the extreme. My 15 year old home is worth 5x the price I purchased it at. That actually scares me. I couldn't afford my home today and I can't afford to really move into a nicer home in the future.