Rent controls work if and only if there's sufficient authority and incentives to motivate developers to grow housing inventory vertically (skyscrapers) and/or horizontally (sprawl + public transport) just enough to not have a glut while aiming to approximate the desired rent-controlled price(s) such that there's less arbitrage, gaming, property owner loss and/or exploitation. (In effect, rent-controlling with structural market policies, while providing rent controls as a secondary guaranty layer to protect renters, especially vulnerable populations.) Housing is one of the more inelastic markets because everyone needs it, and so even minor constraints in supply can rapidly lead to price spikes.