I'd count that as a plus. If a government is the only one that the method to refine the metals used in coins, then they're very difficult to counterfeit.
That's a good point, actually. Coins made from a process and material that can't easily be duplicated would be very useful as a currency.
Only for someone who's worldview is distorted by living in a world of fiat currency.
Historically, the value of gold was based on weight and purity, not whose head was stamped on a disc. That's the virtue of commodity money, and why it makes sense to measure gold coins in fantasy games by weight. If you have a chest full of 10 pounds of gold, that tells you everything you need to know about how much treasure you have. The type of coin and even the count just becomes flavor.
The main reason why some coins were preferred over others in the past was trust. If the country who minted a particular coin put in protections like ridges to make filing or other cheats obvious, was known for not debasing their coins (diluting the gold with some less valuable metal), and aggressively went after counterfeiters, a random merchant was more likely to accept the coin because it was a safe bet that the coin was was worth its face value. Otherwise, merchants would have to test the purity, check to see if the coins were just plated, weigh them, and so on. From a game standpoint, you could roll to see if a batch of coins were debased, plated, or whatever; and then have another roll to appraise their true value. Certain well regarded types of coin would be highly reliable, while others would be more suspect, and unknown coins would be unknowns until verified.