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You can actually do it in the US to an extent. Basically create a LLC with owners masked. Enable an authorized user to be an attorney and register with bank. Then use bank and routing number.

You can also use crypto and have a crypto wallet.

Prior to 9/11 it was far easier and widespread among elites to have effectively anonymous bank accounts.

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Considering the evil those are used for, I would consider it more dystopian than a government sponsored bank account.