In essence, the USD had value within it and can be stored.
the USD is subject to inflation.
That is contradictory.
A "store of value" is a technical term used to define something that can maintain or increase your purchasing power. Fiat currencies that are all subject to inflation (ie. lose value over time
and decrease your purchasing power if you hold them) are NOT store of value, therefore cannot be called money. Fiat is only medium of exchange.