Interestingly, this (transfer wealth between each other instantly without fees) is reality in many European countries. I have an app which only requires the other party's phone number, and if they have the same app (many, if not most, do), money is transferred in seconds with a few clicks. I can also get the same thing done by using my bank's mobile app and a bank transfer. Sometimes there is a delay depending on the banks, but the euro-area banking system will allow real time transfers between countries in the near future. At no cost to the customer.
(Of course, the customer will always pay one way or another, but there is no transfer cost.)
And no, banks have not gone bust.