plus - why would people make a change to something that's the same as the thing they are changing from?
Well, it is different.
As I suggested in the hypothetical, Govcoin is more user-friendly, and has the full endorsement of the political parties of the given territory. It also benefits the State in its design.
Even if not for the ergonomics, maybe other coins are ignored, dismissed, or outlawed by the State.
It's the same reason USPS is still around, and that we have public schools even though private ones exist.