Your are incorrect.
Famous example, Spanish pieces of eight were the de facto currency in the colonies early 18th century.
But they had different exchange rates everywhere. The same coin was worth a different amount in Boston, New York or wherever.
And it was a big problem because the actual official payment Network was English silver. It was so much a problem that the queen enacted a proclamation to try and standardize it.
But the standardization just became a THIRD different payment Network based on Royal decree.
People now had to establish whether they were using the Spanish network, English coinage or the official legislated exchange rate.
Three different silver networks in one place.
And of course the actual people are using something else for regular transactions. Bits of copper, tin, script or wood.
During this time every local borough (sometimes each neighborhood ) in England had its own pocket change minted by whoever seemed respectable for daily transactions.
The idea that all money returns to one is a myth.
What we actually see is large empires can keep together large-scale payment networks for 100 years or however long they last, then they fall apart.
That's the historical record.
