US Bank account without physical address (neither personal nor business)

I'm OK with a personal visit.

Just to make it clear: I'm not asking about ways of opening a bank account remotely - while that would be great, I've given up hope on that.
Though, as a side note, it's actually possible if you have a physical office in the US: Open a European bank account with HSBC and you'll be able to open a US account from the same European branch. They do perform a visit to your US office, however, so no ways to get around having that.

Thus I've made peace with having to fly to the US, unless there is another digital bank option akin to Transferwise Borderless.

Well, Transferwise Borderless is a valid solution - for now. You can have an account in EUR, USD and many more currencies, and they're currently not participating in any exchange of information. I doubt, however, that that will last.