The state could already force people under their control to sell commodities to their soldiers for clay tokens. Why switch to gold, a much more difficult resource to obtain and produce coinage with? Was clay suddenly no longer convenient for some handwavey reason because we're now in the Axial Age, despite being used for centuries before? That's the gap in Graebers book that I don't think he covered adequately.
The reason was because now the various city states needed a way to convince people outside their jurisdiction to also provide goods and services for their wars, and those people could not be cowed into using clay. Clay only works within a states jurisdiction because they could punish counterfeits and ensure it's value among subjects as a tax credit to the state. Outside a state's jurisdiction, foreign soldiers have no guarantee that those clay tokens will continue to be a secure store of value. What if the state you were fighting for collapsed tomorrow? Now their tax credits are worthless. Gold, on the other hand, holds it's value because people like shiny things regardless of which king is stamped on it. But because the gold is issued by a state with their tendency for standardization, now your gold trinkets come in nice standardized units instead of a random assortment of jewelry, what gold would have been used for previously.
The reason was because now the various city states needed a way to convince people outside their jurisdiction to also provide goods and services for their wars, and those people could not be cowed into using clay. Clay only works within a states jurisdiction because they could punish counterfeits and ensure it's value among subjects as a tax credit to the state. Outside a state's jurisdiction, foreign soldiers have no guarantee that those clay tokens will continue to be a secure store of value. What if the state you were fighting for collapsed tomorrow? Now their tax credits are worthless. Gold, on the other hand, holds it's value because people like shiny things regardless of which king is stamped on it. But because the gold is issued by a state with their tendency for standardization, now your gold trinkets come in nice standardized units instead of a random assortment of jewelry, what gold would have been used for previously.