Originally Posted by ChocolateFactory

Can't comment on France/Italy, but the German process being "convoluted" is simply a result of legislation.
German KYC/AML law requires financial institutions to verify their customers' identity. With American Express, you can't walk into a branch to show your passport and residence permit - as there are none.
In theory, they could do address verification via credit bureaus (SCHUFA etc.), but they can't/aren't allowed to verify tax IDs (whereas I believe US credit bureaus do that).
I'm sure you don't want anyone to be able to open bank accounts or credit cards in your name, simply because they found out your address. ;-)

So the only way to do it is PostIdent - which means you show your passport to an employee of any post office. Which is still a hassle, but at least there should be a post office even in small towns.
Or you can do this VideoIdent thing, which means you just wave your passport in front of your webcam, so you don't even have to leave the house.
(In theory, the German national ID cards are smartcards. So you could get a chip reader and use that for identification. But as Germans are paranoid when it comes to data privacy, almost no one has that feature enabled and so almost no bank cares to support it.)

Yes, it's more convenient in places like Scandinavia where you just log in your country's official identification system (BankID in Norway etc.) using your tax ID number and the bank pulls your address right from the tax office's official residency register. But after experiencing dictatorships twice in a century, Germany are a bit skeptical paranoid when it comes to centralized data storage.