Is it even possible to build new housing when the population density is already at 20k people per square kilometre, like in the cities mentioned?
> Also the fact that it's so expensive and people keep moving there shows that it's an attractive way to live.
Did you consider that not everyone has a choice in the matter and the alternative is often unemployment? There's a trend towards urbanization because people move to where the jobs are. That alone doesn't make any place more livable.