Right, written documentary evidence since Roman times shows that currency was measured by count not weight. There was a brief aside in medieval continental Euro

Right, written documentary evidence since Roman times shows that currency was measured by count not weight. There was a brief aside in medieval continental Europe when some influential policy makers misinterpreted Roman documents, but by that point the currency was well established. The value of the constituent metal is dictated by the price (in count) that the mint pays. Nobody pays less because you could go to the mint, and if anybody demands more, you just melt the coin. It was the count that gave value to the metal, not the other way round. The only evidence for currency from barter comes from the imagination of economists of a particular bent.