I've lived in Berlin for 10 years now. I moved into my place 10 years ago this month and the rent would definitely go up without the rigid German laws to prevent exactly that. By at least about 30-40% I would estimate. That's walking distance from major landmarks like the Alexanderplatz, the Berliner Dom, and the synagogue on Oranienburgerstrasse. I pay a lot by Berlin standards but I live dirt cheap by any other standards. I don't know many places in Europe where I could live this cheap and that centrally. Around 950 euros a month for an 85m2 place, including heating cost. Very nice deal. You need to move quite far out of the center of most European capitals to find anything similar and forget about it in the bigger ones like London, Amsterdam, Brussels, or Paris.

However, that's not the point for the locals here. They've seen people move in over the last decades, claim their public space, and as a consequence their cost of living is going up like crazy and they are not getting a lot in return. That sort of thing creates a lot of resistance. There are a lot of people in Berlin that are not big earners. And only a few years ago they were still getting awesome deals on huge places right smack down in the middle of the coolest city in Europe (after 10 years, I know this is true). I had friends paying less than 600 euros for a 100m2 place. OK, it was in need of a bit of renovation but still. Of course that was never going to last. The same place probably goes for around 1500-2000/month now.

IMHO, as a foreign contributor to the gentrification, a lot of the housing shortage is artificial and it has a lot to do with the local legislation that is designed to conserve the status quo combined with the fact that the local government sold out early for way too low to big investors. At this point they don't have a lot of control because they sold out. Also, this city is growing like crazy and it has insanely high dept due to failed projects like e.g. the new airport that was supposed to open in 2012 an will probably not open for years to come.

So, they are kind of powerless to fix things and their political legitimacy is based on an electorate that would favor draconian measures. So, obviously that kind of thing is very popular with the locals. There's no money to build new stuff and besides they've sold all of the land on which this would need to happen. So, the next best thing is populist measures that don't actually solve the problem but make it look like they are doing something.

There actually is a lot of land in and around Berlin. This city is pretty far from other German cities so there is a lot of country side in all compass directions. Also inside the city there is plenty of space. This city still has less inhabitants than before WW II and the cold war (4.3M in 1939 vs, 3.7M last year). Thanks to the cold war it is kind of very spread out with lots of former no mans land, huge parks, etc. People strange to Berlin always ask where 'the center' is. There's no such thing. And there are at least two areas that could lay claim to that and half a dozen more that are probably more interesting in terms of nightlife, culture and other things you would find in most city centers else where. So, lack of land is not a problem in Berlin. Constructing things on it is. And housing projects for lower incomes is not a priority.