It’s funny you bring up opening a bank account in the EU. My girlfriend is French, so I asked her to ask her parents if I can open a savings account in France. This was largely out of pure interest, but if it was a good deal I would consider doing it. Anyway, her father inquired at the bank. They seemed to have no clue about whether an American Citizen (I realize your situation is different) can open an account there. They were completely unhelpful!