People are bringing in the supply-demand curve from their school economy classes. The problem is it doesn't work that way with housing. There is zero incentive to build affordable housing when you can build a luxury house. On the contrary, landlords in Berlin "renovate" all the time, to make normal apartments into luxury ones.

So without regulation, the supply for affordable housing is diminishing. To increase the supply and reduce the prices, one needs regulation. Without all efforts to reduce prices by giving landlords the opportunity to build more affordable houses will be wasted. They don't want this opportunity, they need as much money from each square meter as they can get.

I am all for building more where there is space, it just needs to come with some regulation. That is, a certain quota of social housing in each building, prohibit meaningless renovations, make it less attractive to use property as an investment.

Rent freeze does some of this. It lets people stay in their house, preventing further gentrifying districts (which would lead to further rise in prices in a kind of a positive feedback loop). And what is important, it makes property in Berlin much less attractive of an investment, because nobody knows what else to expect from the senate (even expropriations are discussed).

I don't expect it to solve the problem completely, but it will definitely slow down its progression.