It's not even a thing "in Germany". There may be some banks that do this, but I would say most don't. But then, most banks are relatively regional, so while you can use any branch of the bank, there won't be any branches of your bank if you travel far enough--and if you are with your local Sparkasse, for example, then that is your bank, the Sparkasse in the next bigger city over has nothing to do with them (well, yeah, they have, but they most definitely are a separate bank).

Yeah, my wife wanted to open a separate account for her new job, and they said she'd have to go visit the original branch.

This is at Deutsche Bank, by the way, not some podunk obscure bank.