All that you say makes sense to me. But I have a few questions.
1. How can a nation's currency, whatever the unit, reflect the value of the nation when it can be counterfeited? In other words, if the number of units can be doubled at whim, does the currency still reflect the value of the nation? (Assuming the actual value of the nation remains constant.)
2. Anything can be used as "local" currency within a nation, including no currency at all (barter). It seems to me that the nation's only way to establish a national currency is to deem some unit as the only way to pay taxes. That imposes the currency unit. Do you agree?
The first question is a good one and explains the enormous efforts in making a currency difficult to counterfeit. The tech wave of the last 40 years have made it possible for counterfeiters to create currency that was undetectable from the real thing. So a counter effort in technology was required. And today our US currency looks quite different that it did 20 years or even 10 years ago.
So anti-counterfeiting measures are part of the ‘force’ behind a currency. The USA has the force of law behind the dollar but the US dollar is made valuable only to the extent that the American way of life is attractive.
As to the second question, you are correct. The basis for imposing by force of law a currency on a population is to have a measure of taxes. In early America, tobacco was used as a currency or more correctly as a unit of barter. Tobacco was a good medium for barter because it was lightweight, and its dried state did not diminish its value and it was esteemed. It was used to pay taxes in certain jurisdictions.
Again in reference to the second question, as long as there is an American government, it will impose a unit of currency that must be used by force of law. As long as the American government holds to the ideals of its Constitution, the unit of its currency will have good value.