IDs cost money in Germany, you definitely aren’t required to have it on you (but most do because it’s in the wallet), and technically you aren’t even required to have one you’re only required to have an official identifying document which can also be a passport. Or, if you’re an alien, well, passport, or residency permit. Any Schengen one probably works.

Oh and IDs aren’t required to vote, you usually just show them the piece of paper they sent you to tell you when and where to vote. Push come to shove and things being suspicious you have to “make believable” that you’re you, and that also works with a student ID or whatever.