Exploiting the difference in value of a commodity between communities is a valid way to make a living, traders have existed for a very long time, though if there's little effort required the values will quickly align with each other. Turning it into an infinite money glitch by having a mint convert your raw material into coins is nonsense.
That's all still assuming the coins are made of pure gold/silver for some reason. And assuming the mint is willing to just make money for you in spite what I've already said.
Edit: And that's all if you ignore the fact alchemy, conjuration, and transfiguration exist in that universe so the entire thing is moot anyway. The angle they should have taken is that physical currency makes no sense in a world where you can just summon more, but I suppose that's harder to turn into "I'm so much smarter than the entire world".