You'll probably have an easier time getting one, but you won't be paying much less. I pay €450 for a decent two-room place in a beautiful part of Kreuzberg, and it doesn't go much lower than that anywhere in Berlin.
Although if people owned the flats, the lower income senior citizens would still move: they would find it expedient to sell their now-expensive flats and put the money to living expenses (or grandchildren or travel or assisted living etc). This is happening in other growing cities around the world.
edit: It seems to me renting (or some other form of "right-of-occupancy" arrangement) is actually the desireable choice for most situations. Investing hundreds of thousands in a single unit of housing is not a good fit for most people's savings/investment plan - you'd want to diversify, and possibly hedge against things going downhill in your neighbourhood. If rent market works well, and taxation and rental terms work out, it's better for everybody to just pay for the apartment's financing and maintenance plus a small profit margin in the form of rent.
People usually buy a house or flat only when they are very good situated and are founding a family. And even then most prefer renting simply because you have to take care of less things (owning a house can be quite time consuming).