If a hotel insists on keeping your passport for the duration of your stay, simply politely but firmly refuse. Multiple times if necessary. Get the police involved if they refuse to comply. They are welcome to take a photocopy, but they must return it immediately. No questions asked.

FWIW, in many EU countries, everyone (yes, everyone) is technically required by law to have some form of national ID on them at all times. Germany is one of these countries. This law is rarely (but sometimes) enforced. I have heard stories of police officers in Poland desperate for a bribe (legally) catching out British tourists who left their passports firmly locked away in the hotel safe and not on their person.

If your hotel insists on keeping your passport, then they are hindering your ability to abide by this law and they are (albeit temporarily) expropriating government property without due cause and authority.