All of this seems a lot easier and cheaper than bitcoin's distributed ledger.
The other day I walked into a shop where I couldn't pay by card because the banks didn't provide the service to them. Users don't see "without banks" as a feature, but businesses will. It will reduce their fees and their dependency to the whole industry.
There will still be an intermediary to whom the small business will pay fees for a turnkey solution. And absolutely those fees would be lower in a world where anyone can participate and compete on them. But that's definitely not the world we live in just yet, and even if/when it arrives, I don't think anyone at the retail level (either the consumer or the storefront) will have an appreciably different experience from what they have today.
EDIT: Just adding also, clearing times is the other huge barrier. Obviously no retail environment can tolerate a transaction delay of more than a few seconds, so the other function of the intermediary would be to manage that reality, by some combination of pre-clearing transactions for customers who look safe (classical CC fraud detection where de-anonymizing would be a key component), or maybe a pre-paying scheme (which ends up sounding a lot like a bank debit card).
Most people don't really need or want to take on foreign exchange rate risks.
Banks would become an optional frontend on this transaction system, with security features built-in, etc.