While it is possible there are other reasons, I think one reason they want a US address is for tax reporting. They may need to report your income to your US state of residence, but if they don't have an address for you in some state they have no idea which state they should be reporting to. Thus, while the foreign address could be for the obvious reason, that you've moved overseas, it could maybe also be seen as an attempt to obscure your state of residence to avoid taxes there. They seem to not want to figure out the difference.
My situation is that I'm a former US resident but not a US citizen. When we moved but decided to keep some accounts in the US we found, I think not coincidentally, that the banks where the account was in the name of a California trust, rather than directly in our own names, were happy to take our foreign address, but the bank where we'd opened an account in our own names insisted on a US address; we kept that account only because we had an address we could use.
All the banks are aware we no longer live in the US (or at least that we are no longer "US persons" for tax purposes) since we filled out a W-8BEN and were asked to state a purpose for each account. They don't seem to care, and I'm certain would have even less reason to care if we were Americans. They seem, however, to want to be able to associate the account with a US state in all cases (the trust is a California "resident" even if the trustees aren't), and to demand a US address when the US state isn't otherwise clear.