In Denmark, we have one system, Dankort, which then interfaces with all these funny credit card companies. But the backbone is a single system. There is no reason - other than tradition - that this backbone couldn't be run by the state.
I'd add that it's the same in France, with the Groupement Carte Bleue (which was imposed on reluctant banks by the government) imposing a single set of rules for cards clearing and ATMs. In the long run, we're all dead. John Maynard Keynes
Same with GSM - thanks to heavy-handed regulation at the highest level (in this case Europe), Europe got a better standard, and imposed it across the world. With 3G, industry tried again to impose incompatible standards onto weaker regulators, and the result was incompatible standards and Europe losing its leadership. In the long run, we're all dead. John Maynard Keynes