In November 2019 this was no longer true. I went to multiple branches of WF, TD, BoA, Chase, Santander and Citi and none would open an account for an NRA without a permanent US address. In the cases of Santander and Citi I even had accounts in my home country already and bought documentation with me.Yes this is possible and very easy.
WellsFargo is the bank to go to at the west coast, (deposit $1500 and you do not pay account fees)
TD at the east coast (deposit $500 and you do not pay account fees).
With both banks you get issued a debit card. Your account opening deposit ($150), which you can spend immediately with your debit card.
BoA also accepts walk in customers.
You need a passport + drivers license, and a credit card to fund you deposit (WF) or cash (TD). For both you do not need a US address (you do for BofA). A US cellphone number is easy (for account autentication, you can easily change this to a EU number once you are back in Europe.