They can withhold supply, and that might have an effect on market prices.
It applies more to things like retired people living by themselves in a 3 bedroom house.
Though if they can't withhold supply, how are those cartels supposed to hold up prices, then?
(Except that they can prevent construction of new units through zoning.)
OPEC does that via production cuts. Or rather tries to do that.
The only way they can maintain one is through legal force. Zoning laws are almost entirely that force; they're a way to establish a cartel of homeowners.
They can withhold supply, and that might have an effect on market prices.