You blame Visa and Mastercard for the swipe fee, but they keep almost none of it — the fat cut, called interchange, flows straight to the bank that issued your card, and it barely exists in the countries that built their own payment rails

When a Visa-branded card taps a terminal at a Manhattan bodega and the customer walks out with a $4 coffee, roughly 10 cents of the transaction disappears into the payment machinery. The merchan...