Everyone has to carry around half a million credit cards? Every merchant has to make half a million separate payment processing agreements, each with its own card machine?
No; this is a natural monopoly situation, and just needs to be regulated hard.
There are two providers (more in fact, if you count country-specific providers), and they are interoperable.
Yes regulation are necessary, including for interoperability, but I don't really buy the natural monopoly argument (at least not more than any tech companies).
I don't object to that idea at all. It sounds like Brazil has been having success with that recently.
...Of course, we do need some more safeguards first to make sure that such an entity wouldn't be massively abused by tyrannical executives cheerfully twisting the law into bizarre pretzel shapes in order to attack anyone who disagrees with them.