jmherbenerThese arguments about the technical efficiency of media of exchange miss the point of economic efficiency. To use an analogy, consider the thermal efficiencies of different types of engines. Electric engines may have higher thermal efficiency than gasoline engines, but that does not determine which engine is economical efficient, i.e., superior in economizing resources. To determine economizing or economic efficiency, the only guide is economic calculation, i.e., the profitability of production.
In like manner, to determine the economically efficient media of exchange, one must refer to the profit of its production. The issue of fiat money and fiduciary media are not subject to the test of profit and loss. It is always profitable to issue more of them. Put another way, the issuer do not bear the opportunity cost suffered by others when of issuing more. Neither fiat money nor fiduciary media, therefore, can be part of the market economy. They are foreign elements because their production cannot be determined by profit and loss.
The arguments about the technical efficiency of money falsely conclude that the monetary arrangement that allows people to minimize the holding of money proper (or as you put it, maximize velocity) is the economizing monetary system. This is analogous to someone concluding that choosing electric engines over gasoline engines economizes resources in society because electric engines have higher thermal efficiency than gasoline engines.