Yes, and Hamilton's thinking was dead wrong.
Wasn't the only example either. Note the opposition to his plan, and the reasons.
People have been trying to figure out ways to counterfeit currency for centuries. Nowadays only governments can do it legally. They like it because it's what they use to buy power. Just because the Fed has a history doesn't make it a great idea.
The first coins were made of precious metals. For most of our history, our paper money was exchangable for gold. There was a reason for this.
You're either missing the fundamental point or, more likely, just avoiding it.