Housing is a strictly zero sum game. When you have more people who want houses in an area than there are houses you will have winners and losers.

Rent control chooses certain people to be winners and other people to be losers. It does exactly nothing to increase the number of winners. Furthermore it creates disincentives to the creation of new housing, which means fewer winners in the future. Even worse, for the winners it does select it puts them at a long term disadvantage by trapping them into a non-optimal location.

The only solution to “not enough housing” is “more housing”. Rent control is actively harmful to this goal.