It may “make sense”, but it’s also an ahistorical just-so story.
If you want a more accurate description, I recommend the first half of David Graeber’s book Debt: The First 5000 Years, also mentioned by another top-level comment.
It's a great read that actually gets you to understand how money came to be, in a theoretical sense. The book the other poster suggests is more about the history of money and monetary phenomena.
If you want a more accurate description, I recommend the first half of David Graeber’s book Debt: The First 5000 Years, also mentioned by another top-level comment.