My issue with it is that it won't help with the problem at hand. Sure, it might help tip the scale of rent prices, but lack of units or even rents are not the issue in Berlin. Sure, it's way more expensive than before, but rents are still payable.
The issue is that it's very difficult for individuals to acquire housing units. My apartment costs about 1500x its monthly rent to acquire (€400 vs €600k min). Which means it's now a lousy investment for people wanting to live in it (since they won't be saving any money unless live to be 150 years old), and for people wanting to buy a small number of properties to rent (same deal).
Since real estate is traditionally kind of a "future insurance", for old people not to have to rely on pension to live, it also makes the future a lot grim and uncertain for people who'll have to rely on public pension for a place to live.
Getting more units in the market will only make things worse for those people: rent prices will make it impossible for them to own, and won't make sense for them to own to rent.
Individuals not being able to acquire apartments also has the side effects of things like crazy rental terms (not difficult to see the best apartments with limit of 6 months rental) or even empty units because they're used for commercial renting only. Across the street from me there's a 50-unit condo that's fully empty. I know that because I used to live there and for a while I was the only tenant. It costs about €2000 a month vs my €400.
I don't know what's the endgame of speculators. Maybe they're waiting to own everything so that they can jack up the prices? Maybe they're merely taking opportunity of the low interest rates to pay for those things in 100 years? Is that investment companies buying it to force people into private pension?
I don't know. I just know that the issue is a lot darker and I don't see "the market" solving it by itself without creating even more problems. I know this is a very sensitive matter to some people but I just don't see "the market" doing anything positive if left by itself.
EDIT: As user probably_wrong put below, "the losses would be socialized (namely, the park) while the benefits would go to the wealthy."