I'd prefer those over public housing very much because only with them, the interests between the renter and the landlord are aligned, and they're not part of the state and can therefore not be used (or sold) by political decisions.
* Typically in Germany, social housing is built with a time-limit built in: after X years, the house falls out of the social housing program and can be rented and sold freely. At the moment, a lot more houses leave the system then are added.
* Many cities sold their real estate after the financial crisis to give the money to the failing banks. I.e. Berlin is super-broke, in parts because of a big banking scandal of the previous government.
* In Munich they have a pretty decent system: anyone who develops land had to keep to a certain split of social housing, middle income housing and free market housing. They use the land they own and their powers over zoning to enforce that.
Profit is just an emergent form of social compensation for addressing a shortage. That society enacts laws to prevent the profit motive from working, and incentivizing socially beneficial behavior, is a tragedy.
As far as I know, it's a widely discredited theory, never based on any actual studies.
Or politicians are corrupt and Thatcher is a good excuse. Take your pick.
On top of that, the Conservatives made an election pledge to build 200,000 starter homes in 2015 election and apparently failed to build a single one. It's easy to claim you'll build houses and then do nothing, like it's easy to claim you'll reduce immigration but it just keeps going up.
The last election in 2019 was mainly about Brexit and the general public's perception that Corbyn was unsuited to being the Prime Minister.
(I might be wrong but) if I had to bet why councils could build more places it's that they would have a streamlined approval process with councils (denying a social housing project would look bad) while the private developers have to follow the mood of the deparments and several "appeals" and "NIMBYs" (same as in the US today)
But a new "luxury apt" opens a place in a slightly cheaper property.
In the 30 years since then, the most they've ever managed is 30,000.
It's not in private landowner's interest to build cheap social housing. It reduces rents, it suppresses property values. So they don't get built.
If they do build anything, it's in their interests to build luxury apartments. They make the most money out of those. I know little about Berlin's housing, but by any chance would there be a lot of expensive apartments being built?
Did something similar happen in German history? You'll probably find all the big landowners in Berlin and Germany lobbying very hard to make sure nothing like this ever happens.