If price levels were higher wouldn't greedy and ruthless apartment builders build more apartments?
Only if there was somewhere to build them.
No matter how much money I give you, there is a (very low) limit to the number of new apartments you can build in central Stockholm.
Money has ceased to be the limiting factor on the number of dwellings; so the number of people who can have apartments is capped. The question then becomes 'How do you pick who gets one?'.
You can give them to the richest applicants (the market solution), effectively excluding poor people from the area;
You can give them to the people who have waited longest (the rent control solution), effectively excluding new people from the area;
You could have a lottery every time one becomes available; there are lots of ways to choose.
Using money to determine who gets a scarce resource is a good idea, when more money can lead to more supply. But as that's not the case for apartments in fully developed inner city areas, it is no longer necessarily the best solution.
The mark of intelligence is recognising when a really effective technique has reached its limit of usefulness, and needs to be modified or even abandoned in favour of something new.