Yet in the US, it was developers following the Levittown model that resulted in tons and tons of single family homes, so I fail to see how the free market is terrible at "pumping out houses fast"?
In my old neighborhood, if a developer wanted to build a high rise with 300 apartments, they’d make a proposal for 350 apartments, have a few public meetings, let people yell at them for a couple hours, and make a “concession” of reducing the project to 300 apartments. Then everyone goes home happy. Everyone knew that was the game, except perhaps a few obtuse NIMBYs that thought they were accomplishing something.
In the mile or two south of Roosevelt Rd, there are 5000-10000 permitted apartments/condos, just waiting for some developer to get a loan and pull permits to start construction. No public meetings needed. They could start building next week.
The average rent in Berlin (and other German cities) is not very high but that's because a lot of flats still run on a very old contract. If you're moving to Berlin, finding an apartment is incredibly difficult, even if you're willing to spend a lot of money. My grandmother lives by herself in a 90sqm flat in a really nice area and pays 400 Euros a month. In the last 10 years she tried to find a smaller flat (30-40 sqm) for herself but the cheapest she could find was 750. So she stays where she is and just doesn't use 2 of the rooms she has except for storage. In the meantime, a friend of mine moved to Berlin and couldn't find a decent 60sqm flat for less than 1400 Euros. The only way to get those affordable rents is either knowing someone who is moving out or getting super lucky by finding and getting it through a public ad.
Massenbesichtigung (mass viewings) are not uncommon. The agent will publish a public timeslot and literally hundreds of people lined around the block will show up to view a single flat.
It costs a lot of money to build a new apartment building because land where you are allowed to build is regulated by the State. Also the State requires many regulations that increase unnecessarily the costs, and most of all in the name of the ideology.
For example, housing standards of Japan and the US, which are way cheaper and still serve two of the richest countries in the world, would never be allowed in Germany. That makes housing unaffordable and drives people into poverty.
I live in Japan, so I know it first-hand.
Housing standards in Japan are awful. The average Japanese city is chaotic and ugly with zero urban planning, and the average Japanese house is built with the cheapest possible materials and has zero insulation. I remember reading that the average Japanese house uses 7 times more energy than the average German house! You do NOT want to build houses like Japan.