Mass fiat money are no more than 2 centuries old, in most places less than 60 years (see Bretton-Woods). They have to be tightly controled by state.
If the value of the coin come from the gold in it, why mint them instead of using the gold directly?
But coins show the insignia of the state (and usually the monarch) that minted it; this is an important symbol, and also a guarantee of purity and weight, at least nominally.
I don't think you're considering a long enough time scale, the minting of coins with the likeness of rulers and symbols of the power of the state is as old as the concept of currency and rulers.
There have been instances where companies printed their own script and new non-authoritarian nations might struggle for a bit early on with competing banks, but it's always resolved and power is vested in the central authority.
The role of currency from the point of view of the central authority is more than just economic - it's symbolic, it's propaganda, it's confidence in that government expressed by every citizen through the very act of accepting their currency as valuable.
Universality of your currency is kind of the best selling point isn’t it?
Also, barter worked very well since forever, in which every product is a different "coin", it just doesnt scale physically, while digital currencies do.