A market response to supply and demand is illegal? What law would do that if not a rent cap?

§556d, 1 of the German civil code.

https://www.gesetze-im-internet.de/bgb/__556d.html

It's illegal here to demand a rent more than 10% higher than the "ortsübliche Vergleichsmiete", which is approximately the local rent averaged over the last 6 years (exactly defined in §558)

More generally, you cannot simply ask for astronomical prices for anything in Germany just because you know that people are in a position where they have to pay them, that's "Wucher" (racketeering) and against public decency, which is generally illegal according to §138.

https://www.gesetze-im-internet.de/bgb/__138.html

Interesting. That sounds a lot like rent control if the wiggle room is only 10% over a 6 year moving average.

It is rent control - which basically exists throughout Germany. Even in SF rent controlled apartments can increase some % per year, it is just controlled how much. In Germany this is often done by looking at the region's average price for similar properties and then fixing some limited increase against that. This is distinct from the rent cap that was overturned, which stated no rise in rent at all for five years.

There are multiple kinds of rent caps. One is the maximum annual raise for existing tenants.

Another one is vague and based on the "Mietspiegel", which lists appropriate rents according to quality and location.

If the rent exceeds this by too much, you can sue for "Mietwucher" (rent usury).

Rent control prevents from increasing by more than a set amount every year. Theoretically you can wait for decades raising the rent every year

§ 291 StGB Wucher