Once additional supply is added, all the dynamics change though. The cartel can restrict their own supply at the price of profits, but cartel members will see that investors who are not part of the cartel enjoy the same high rents while having much higher utilization because they don't need to keep flats empty. The only way for the cartel to ensure that doesn't happen is to either make sure every (new) landlord becomes a member, or make sure there can be no new landlords.

So far, they've use the latter option, and that's most likely because the first one is hard: if the cartel controls the market and keeps the prices high, new investors have no incentive to join, they'll make more money if they don't.