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.
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.
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.
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?