“And foreign banks would comply with nosy American regulations for what reason, I wonder?”
At a guess, reciprocal treaties requiring that specific types of laws are honored. I know there’s an agreement with every country on income taxes. If you’re a US citizen working almost anywhere you pay US taxes (which are a bargain.) Foreign nationals in the US are supposed to pay their country’s tax.
European banks are under no compulsion to open or maintain accounts from anyone -- treaties or not.