Rent control generally only controls increases, not absolute prices, and is relaxed for newer constructions, so developers care less. At the same time, it may reduce the cost of land zoned for high density housing if locative uses are judged to be less profitable, thereby reaching and equilibrium. It also often lowers market rent for everyone, when implemented correctly.

We can measure this reluctance by looking at construction rates and general supply in similar groups of cities or neighborhoods with or without rent control, of course controlling for other variables. This has been done in multiple studies, which are listed in the link I provided.