People used gold and silver coins from foreign mints, but they had been clipped so many times that a merchant had to weigh the coin to figure out how much metal there was in it. They even cut the Spanish Milled Dollar into eight pieces for commerce.
On the frontier, it was even worse. Coins did not circulate far beyond the cities, so the frontier was on a barter system based on brewed and distilled products like beer, ale, porter, stout, whiskies and brandies. The frontier was literally on the Alcohol Standard. A barrel of beer or cask of brandy could be traded at a trading post for gingham or hemp cloth, a side of bacon or machine tools. This was why the whole Whisky Rebellion situation was such a mess. The Brits had taxed brewing and distilling apparatus, and now the new federal entity was doing the same thing. No wonder farmers were up in arms!
Hamilton's paper money scheme was the only thing that would work, especially considering the need to park money in something safe for professional capitalists.
I think you're being unfair to Hamilton. He inherited a mess, and his solution was the only thing that would work until this nation could secur its own source of gold.
I appreciate you providing some more information. Well worth considering to learn more about the period and men in it.