There is actually some internal logic to minting coins that are not made out of metals with intrinsic value equal to their face values. If the population doubles, and the amount of gold or silver in the world remains the same, then you actually have pressure towards deflation, because the static amount of precious metal has to be spread among twice as many people.
Money, in whatever form, also serves as a way to assign value to labor, and as a medium of exchange. When you put out one hour of labor, it has to have value assigned to it in some fashion. The best case can be made for increasing the money supply pari passu with the value of labor and the population. But that's not possible if you are working with a large static amount of precious metal in the world.
And, yes, precious metals can be extracted from the earth, but probably not enough to keep their value in sync with an increasing population.
I know nobody wants to give power to a government to issue ever-increasing amounts of money by fiat, but it's hard to see an alternative, at least as long as the money supply keeps pace with the population, and money isn't just issued wildly out of proportion to the population and the strength of the economy. That's what's driving inflation right now, with more and more money being created and churned into the economy, with increased prices being a way to soak the money back up. Just look at Weimar Germany and Zimbabwe.