To be honest, the amount of time it would take to co-ordinate that a government would probably just wear the loss to counterfeiting. In the FCoK the currency was changed every few months to stop stockpiling and you could also limit how many were exchanged for food every day.
You would still have to exchange notes for ones of teh new design or you'd be choking free enterprise (you may not see this as a negative), or have a way of swapping surplus currency for some other sort of benefit. Capitalism might suck in some ways, but if a government wants a recovery it's going to have to stimulate the economy in some way.
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