As someone who has a few bank accounts in different countries of which I'm not a resident of, and also a user of the services you mention, its next to impossible to use them for banking purposes.

In US, for example, their addresses are classified as Commercial Mail Receiving Agencies, and have a "Commercial" address designator. USPS has an API for that. If you get a bank to accept this address somehow, then the next trouble comes - they're gonna ask for utility bill for address verification and you can't have any utility bills for it.