The issue with your solution still comes down to yet another centralizing middleman with no real incentive to be efficient. And all the incentive to lobby governments and extract more wealth from the people.
This can of course be done government by government, but that isn't scalable for a global company.
It doesn't have to be 1 middleman. Multiple companies can issue the cards, just like there are multiple beer and cigarette and lottery companies.
I wish I could edit my post because a lot of people had the same misconception when I first wrote it.