Rent control does little to discourage building in fact (1). One of the biggest, and imo only agreeable argument, against rent control is that leads to higher rents on uncontrolled units. However, if an entire region is under the same rent control, that just wont happen. A 7% cap I think is still very generous for landlords. It's probably still well above the rate of wage growth, though.

https://dornsife.usc.edu/assets/sites/242/docs/Rent_Matters_...