Why exactly should they? I mean, I don't want to forcibly remove them, but there are many cities in Germany other than Berlin.
If one city is getting richer and richer, then the average price of an apartment goes up. More rich people start comming, because they see oportinity to do business there. At the same time poor people have a choice of moving to smaller, more affordable cities.
The biggest pitfall of a mankind is that we cannot grasp that the world is constantly changing. Life itself is a process of constant change. Just because your parents lived in Berlin and you were born in Berlin does not imply that things have to stay this way forever.
Trying to stop the flow of time and inevitable change is what makes us miserable.
Why hasn't anyone thought of this before!