When reading about economic theory, one of the arcane areas of argument that comes up is the origin of money. From the perspective of knowledge for the sake of knowledge is a good thing, one cannot complain about this. However, if you are interested in understanding the current monetary system, this debate is largely a red herring. In this post, I discuss some of the criticisms of "neo-Chartalism" by Anwar Shaikh in his new book Capitalism (link to my discussion of that book).The simple answer to the importance of the history of money in theory of money is historical. Neoclassical economics is based on the barter-commodity theory of money, which implies that money is a neutral veil.
The opposition of some economists to this deficient assumption was not only to point out that money does not function as a neutral veil in modern monetary economics, but also that the narrative on which the barter-commodity theory of money is erroneous. For example, the commodity theory leads to the assumption that gold is money, or gold, silver and copper are money, and that other forms of money are just tokens for these real assets.
So, yes, economists have to take the history of money into consideration into order to avoid the false assumptions that afflict conventional economic methodology, a principal one of which is that a modern economic is a barter economy rather than a monetary economy. This has lead to wrong conclusion and disastrous policy based on them.
Should We Care About The History Of Money?