At some point you’ll run into construction cost limits for multistory dwellings. I don’t know how close Berlin is to that point but given how much cheaper their rent is than other major cities they’re probably doing a better job than most of building housing.
Berlin is not close to this tradeoff point. Tokyo's special wards have a population over twice as large as Berlin in an area about 2/3rds as large as Berlin.
There's a good reason most of the most-expensive places are on tight costal areas like SF and Manhattan, where outward expansion is possible without making any positive internal changes. Just constantly pushing out from the middle via gentrification instead of any realistic market development to match demand.
Not to mention NIMBY-heavy political systems which are common in urban areas... they are always extremely hostile to new development. Which of course benefits current residents in the short term but is a disaster for everyone in the long run.
> At some point you’ll run into construction cost limits for multistory dwellings.
And Berlin is light years away from that. A 30 storey apartment building there is already counted as a "skyscraper," while Chinese are about to start talking about 50 storey as "a new norm" in some more expensive parts of the country.