In the case of Stockholm, you can usually switch one rent-controlled apartment for another, so the mobility is around the same in rent-controlledd as it is in any other part of the housing market. Obviouly changing cities (thereby markets) doesn't work, but in the case of Stockholm other cities would't have the same problem so moving out would not put you at the back of a 10y queue.

Controlled rents isn’t a bad solution to the economic problem of optimal supply or demand. It’s one of several possible compromises on the ideological scale between “housing is a right and not a commodity and a mixed income city is a goal in itself” vs. “housing is a product like any other and optimal markets solves the problem best”.

The reason Stockholm seems very close to the first despite having one of the world’s most liberal market economies elsewhere is because it’s not easy to change. It’s likely to change but it will take a long time. The right wing parties in Sweden (market liberals) have worked around the problem by ensuring the apartments are converted from rentable to condos instead, because removing the rent control entirely would be too difficult. There is also talk about allowing market rents for new production (it’s already allowed in a limited way).