While your assumptions about barter societies are pretty much true, I think you're off on the origins of currency being tied to force. This is overly influenced by modern fiat currencies whose values are derived from government requirements rather than valuable assets. There was a long period of time where precious metals and other valuable items were used as stores of value without a central authority requiring their use. People used official coinage because its weight and purity was standardized and it made things easier, and the value changed alongside debasement, often in spite of official attempts to prevent this. People also used different currencies alongside each other based on their weights and purities. The only times in ancient societies where we have something similar to what you're describing where a specific currency must be used is in taxation, and even then, most taxes were settled in equivalent values of other goods and not specific currencies. The only example I can think of for what you're describing is the Jewish temple offering system in the second temple period, in which certain obligations to the Temple were ruled to have to be paid in Tyrian sheckles specificall

But what do you mean? We have multiple currencies today? Each one is still based on force within its jurisdiction. Yes people try to get around the law. That doesn't change the nature of force. People speed all the time. This is not evidence that the government does not have authority over the interstates, rooted in force.

Sure it's evolved, but I don't see anything in your comment that really disputes the tie to force. Of course, taxation is connected to force. Additionally, as I addressed in another comment, a lack of modern "central authority" does not mean a lack of connection to "force" or violence. People can come up with distributed or atomized versions, which nevertheless arise under a similar tradeoff with respect to the fear of violence.