You are required to be able to ID yourself, “Ausweispflicht”, but that does not require you to carry your physical ID with you when leaving your house, it just requires you to own said ID once you reach the age of 16.
The cops will still take you with them to the station when you don’t have an ID to show if they ask for it. You are by law required to identify yourself with a physical ID.
So yes, while it’s not illegal to not carry your ID on you, it’s still to your own detriment if you cannot produce it.
You are required to be able to ID yourself, “Ausweispflicht”, but that does not require you to carry your physical ID with you when leaving your house, it just requires you to own said ID once you reach the age of 16.
https://www.deurag.de/blog/mitfuehrpflicht-des-personalausweises/
The cops will still take you with them to the station when you don’t have an ID to show if they ask for it. You are by law required to identify yourself with a physical ID.
So yes, while it’s not illegal to not carry your ID on you, it’s still to your own detriment if you cannot produce it.