It seems to be a very American thing to not have banking as a basic right (or at least assumed right).

Here in New Zealand, there's pretty much no restriction on getting bank accounts. It's almost unheard of to not have a bank account.

Transaction fees aren't really a thing either. Most people only have to pay to withdraw money from other banks ATMs. There's no fees for bank transfers (regardless of whether it's to the same bank or a different one). Bank transfers are within the hour in the same bank, and either within the day or overnight for between different banks.

One thing that definitely has helped in this situation (somewhat counter intuitively) is that we have an oligopoly of banks, so standardisation and cooperation is simple. That's why we have chip and pin cards as standard here (and contactless cards). It's also meant that almost everywhere accepts EFTPOS.

Hell, I had to cash my first check ever today. I don't even carry cash, unless I have a specific reason to need to carry it.