Germany is noutriously slow to build, and as a result there are stark housing shortages in the big cities. Partially it’s due to the German affinity to bureaucracy but otherwise the local quality of construction is actually high (and therefor buildings take a long time to build).
However with rapidly growing urban areas that already experience housing shortages and soaring rents & purchase prices there is no other solution than to dramatically and swiftly increase supply.
Also rents are controlled[1] so it can be a bit deceptive - they are cheap but if you go to a viewing for one of those units you will find yourself as one of 50-100 applicants. And if you want to buy your own flat those prices are not controlled.
Additionally, remember that salaries are a lot lower than in the US, and that at least in Berlin there have been ~10% YoY rise in real estate prices for 10 years now & even those (mostly-controlled) rents have increased 6-7% YoY every year for a decade.
[1] https://www.thelocal.de/20180214/controversial-rent-control-...
Sounds like we should be building more of these in our cities to increase the housing supply.