I have been flying internationally between Germany and other Schengen countries about ten times this month and have not had to show my passport to any German police types or airlines this month.

As an ordinary US citizen visiting Germany, I am technically required by law to have my passport available when in Germany. However, there are some circumstances where technically such requirement may not necessarily be legal. It is easier to have the passport around if dealing with the police, although visitor passport loss/theft is a greater problem when the passport is on the move than when the passport is in a fixed location.