>Also had to show ID (passport, in my case, as a visitor from the US) to board planes in Europe.
If this was a Schengen (inter-europe flight), the only reason you would need it would be on checkin if your airline checks this for revenue protection. By law there shouldn't be any passport checks (at least only randomly).
Anecdote: Travelled by airplane within Europe multiple times, never had to show my passport
>While traveling on trains in Germany, I was also required to show ID.
Which is only required if you get a non-transferrable online ticket. If you buy your ticket at the station, there is no need to show an ID on the train (in contrast to Amtrak)