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.
The GP's point is that it gives equal chances to tenants to stay. New tenants do not benefit from rent control, they instead are hurt by the higher prices due to lower supply.
It's regulations and NYMBYs that prevents any new building with higher occupancy.
Rent control reduces development revenue.
They both play a part in making building development less attractive, just from different sides.
The reason mature European economies do not come close to entrepreneurship and the rate of innovation in the US economy is because widespread govt regulation and taxes across the board stifles economic options for investors.
It is simply not true that housing and employment laws in other places "works great", it's a tradeoff, and if the US follows that path the world will become a less good place for everybody because Europe and Asia will no longer have an innovative capitalist petri dish to follow and leverage from.
Rent control does the opposite. It radically reduces choices and increase on price on people looking for a place to live.
Rent control chooses a small handful of existing renters to be winners. And it makes everyone else a loser. Except it's also shitty renters, because it traps them in place. Sure it gives them a home somewhere. But it denies them opportunity to move to another city, or even the other side of time, to pursue opportunity.