Rent control unbundles the bundle of rights that is property ownership. The result from the renter's perspective is a hybrid between tenancy and ownership.
It's not the only way to unbundle it either. Consider the more traditional life estate, for example.
I’ve lived in a two bedroom rent controlled apartment in San Francisco for the last 7 years. I pay significantly below market rate for rent. I also have enough to afford a down payment on a house here.
Their is no incentive for me to purchase a house unless I lose my rent controlled apartment and even then I probably wouldn’t buy. I know many of my peers who are in similar situations. I’d say the same is true of NYC.