For "banking" take a look at State Department Federal Credit Union, Service Credit Union, and Alliant Credit Union. They all have specific membership requirements that allow people in certain groups to join for free. But all three also have additional affiliate membership options that allow pretty much anyone to join for a low one-time fee. They all allow US citizens to use a foreign address as your residential address. In some cases, you may be able to open an account from abroad. But, it's usually easier to open an account before moving, then change your address later especially if you need a credit/debit card mailed to you.

For brokerages, IKBR and Schwab (specifically their international division) will both accept US citizens with foreign residential addresses. I've heard that other major brokerages like Vanguard and Fidelity will too (with some caveats). But, as you pointed out, once you put a foreign address on your account, you may be restricted from purchasing ETFs and other types of investments due to a combination of foreign "investor protection" laws and/or broker compliance policies. (You can still own these investments. You just can't purchase new shares.) If you have a RIA you can bypass the legal restrictions. But, of course, you'll have to pay for that privilege.

I get the thinking behind continuing to use a US address while living abroad. And for brokerages, the argument is even stronger. But, the terms of service for most banks and brokers are pretty clear about reporting your actual residential address. For me, the risk of an unexpected account restriction or closure isn't something I want to worry about.