FWIW - the large national banks, such as Commerzbank, will let you open a bank account. Of course, there’ll be extra forms to submit your SSN/Tax ID. This is required to combat money laundering and to report the existence of the account to your home country’s revenue service (= IRS).
I can state from experience that they are quite capable of mailing statements to the U.S., but, of course, you would typically use paperless delivery instead.