It may be well known globally, but rent controlled apartments make up ~1% of the housing stock. In order to have a rent controlled apartment, the building needs to have been built before 1947 and it must have been continuously occupied by the same family since at least 1971.
Rent stabilized apartments (IIRC, there are ~800,000 of them including mine) are only in buildings built before 1974 with more than six rental units. What's more, rent increases are set each year and can range anywhere from <1 to >5%. If the owner spends a certain amount on renovations to a vacant apartment, the rent stabilization law no longer applies and the unit can be rented at market rates.
Yes, there is significant regulation of rental units for ~30% of the rental stock, but beyond that it's whatever the market will bear.
Edit: Removed incorrect information about rent caps on rent stabilized apartments.