pilotchute, you can still open bank accounts as a non resident alien.
Apart from sounding like a character from the tv show ALF, it is easy to do and you dont need a social security number or even a us address, just a legit reason for doing so.
The trick is finding someone in the branch who knows how to do it, and I suspect the default position from those bank staff too lazy to go to the bother is “it can’t be done”.