What is your definition of rent control working? There are some studies showing that rent control does work to minimise displacement of tenants [1] and that tenants seek more repairs [2], even more of lower income classes.
If you define as achieving market efficiency, maybe that's not the objective.
It's like unionising, it may make companies less market-efficient by giving more power and control to the workers. Rent control affects landlords by giving more power to tenants.
Building more houses, etc., is an orthogonal issue to rent control.