Berlin population only grew by ~250k people ... since 1990, and back then Berlin was basically depopulatedok, fair point. so berlin does have other options. but the rent problem is not only in berlin, and other cities don't have that space. and nevertheless i stand by the claim that even if more rental units are going to be built in that space, rent prices will not go down without any additional effort.
a good example of doing it better is vienna. somewhat similar to berlin, population was shrinking until the turn of the century. down to 1.5 million. then suddenly in the last 20 years it grew back to 2 million. faster than berlin. vienna government itself is building new housing (a program that started 100 years ago). and infrastructure with jobs to go with it. 25% of people in vienna live in government owned and subsidized housing. (apparently berlin has something similar, but it is privately owned with a government mandate)
Once that area is sufficiently developed
ignoring the option to work remote, if an area doesn't have jobs close enough to easily reach by public transport i am not going to move there, no matter how attractive the rent.