Rent control does keep rent low. What it creates is a supply problem, which could possibly explain the decades-long wait list for an apartment in Stockholm.
Those queues are for public first-hand contracts. You can always rent second-hand (for up to 2 years, from a private owner), private first-hand (more expensive queues from development firms), company rentals (in some cases, your company can be a guarantor, and you rent like a commercial entity with no time limit or deposit, etc. but usually higher rents), or you can buy a place.
The issue is there aren't enough first-hand contracts, or enough properties in general. But the rent controls as discussed only apply to first-hand contracts, which are the minority.
It potentially creates a supply problem, if certain assumptions are met.
However those assumptions rarely hold in practice. In the US, to get a construction loan, you can't assume a big rise in rents in coming years. So the financial decision to build new housing is gated by an effective assumption of rent control by the financiers.
There are other things at play. If the low prices were the only thing stopping new houses from popping up, the 5x price increase for buying apartments would have solved all the problems in Stockholm.
The available space for building stuff in municipal Stockholm is what it is, so some part of the supply problem would still be there without rent control, I would assume.
Removing rent control would convert the decades-long wait list into a decades-long struggle to make enough money to afford rent, would it not?
The issue is there aren't enough first-hand contracts, or enough properties in general. But the rent controls as discussed only apply to first-hand contracts, which are the minority.