I am a white German with no migration background and i believe it is not all that beautiful here and I have been checked on various places. The reason is, that it really also depends where you are, because police has the right to check IDs e.g. in places where migration crimes are more likely like railway stations or in a buffet zone close to the border. In other places law requires far more actual reasons or a far more concrete suspicion. But I have also been checked in the middle of the night on a flixbus that got pulled out from the highway at the border between Bavaria and Baden-Württemberg, which IMHO clearly violated German police law.
Oh, definitely. I'm not saying there's no police checks, I'm just saying according to the police officer it was ok to not have with me at all times and leave at home.
Also, when I was outside of the city I live I would bring the passport, and now the Personalausweis...