> And, of course, the Berlin government forces people to register their address

Meldepflicht is in all of Germany, it's not a Berlin thing.

> and allows everyone to query it, because why wouldn't they:

This is highly controversial, for exactly the reasons you might think.

However, this is an "Einzelauskunft", so you get one address per query, and you are not allowed to trade in those addresses or use them for advertising. Also, if you want more detailed info, you have to provide a valid reason for wanting them.