Where I live, we would call laws that allow rents to return to market-rate eventually "rent-stabilization," and laws that keep below market rates indefinitely "rent controls." I think in most of the examples we are talking about, especially in the case of Sweden, we are talking about the latter.
>Do you think people being driven out of their homes and neighbourhoods by rapidly increasing housing costs a problem?
They aren't being driven out of "their homes." They hold a lease to temporarily occupy a residence that is the property of someone else. Nobody likes to frame it this way, but it's what's actually happening.
I want to keep people in the cities they want to live in, but not just for this generation. If we want to let people live in cities they want to live in (even people who already live there), we need to just supply the amount of housing to bring the cost down... which is doing exactly the opposite of "protecting" people in their current housing by locking it down in perpetuity.
Rent-control makes perfect sense for people who receive it. When viewed through Rawls' veil of ignorance, it is obviously, wildly unjust. If we want to deal with inequality in housing, we need to deal with the monetary inequality, and not create a band-aid, like rent-control, that actively makes the problem worse in the long run.
I think the main reason why rent-control is used is that people don't want their city to change, but they don't want it to become more expensive. Rent-control allows people to have their cake, and eat it too. It just comes at the price of creating a type of informal aristocracy.