The main reason new housing is extremely expensive has to do with regulations themselves.

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.