Most currency is created due to the fact that people are already exchanging goods and services and they need a simpler way to do that beyond bartering and the like.
I've no quibbles with your other points, but this nit is worth picking. I recently read a book called "Debt: The First 5,000 Years" which contradicts the usual dogma that money arose to solve the problem of barter. Here is the author's discussion of that point in depth.