Last time I checked (late 2019), Valiant was opening accounts for non-residents, but was politely declining an account opening to most ordinary US tax residents (with rare exceptions only confirming the general rule). No idea, if a Swiss passport helps with that, since I mostly know US folks living here and struggling with bank accounts, but their problem goes away with unlocking of "Swiss citizenship" achievement.
Why, if I may ask, you need a local bank account - just for sending and managing money to your family, or there are some more complex tasks for it? A simple service like
Wise or Revolut provides an essential current multi-currency account with IBAN, covers all international money transfers and currency conversions.