Banking is part of EU universal services. The privacy issue is troubling but large banks in EU can't refuse to offer a minimal free account for everyone.
If any European would help a poor American claim asylum on political persecution, personal safety, and humanitarian grounds, let me know. Did you know that Social Security recipients in the State of Texas aren't even determined in Texas? SSA outsources DDS to Arkansas.
If you can claim all that why haven't you already?
The format is:
John Q. Smith
General Delivery
Fort Wayne, IA 46806
https://faq.usps.com/s/article/What-is-General-DeliveryFurthermore, there are free and reduce rate PO Boxes available in limited circumstances:
https://faq.usps.com/s/article/Is-there-mail-service-for-the...
And, for cases where "PO Boxes aren't accepted", there is a new format street address of the post office works with a PMB or # second line.