Store of value is the whole game, for now.
Store or Value is a prerequisite for it to be a Medium of Exchange.
If, over time it is used more widely as a store of value, it will become a preferred MoE eventually.
Medium if Exchange is a prerequisite for it to be a Unit of Account.
If, over time is is used more widely as a medium of exchange, it will become a preferred UoA eventually.
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This, in my opinion, does not contradict what I said.
Mises and Rothbard are discussing the emergence of money as a concept. Ie why we transition from barter. It arises from the need to exchange goods and services.
I'm discussing the emergence of a new currency.