But their monetary system is absolutely not decentralized.
The monetary system isn't part of the Constitution or government design pattern. A Federal Reserve didn't exist in 1791. That came later. Today, the Federal Reserve and US Treasury are largely independent from the government, because their decisions are not subject to approval by the federal government. And you're right, the money is centralized.
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Doesn't the monetary policy influence the government?
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It influences every government in the world today. It's taken on many different forms over the last 2 centuries, and gone through many fundamental changes. The government design pattern and Constitution haven't.
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