You described the requirements for a medium of exchange, and they make sense. But I don't think that that means "value" necessarily. Value is bread when I am hungry. Or gold when I need to make microchip contacts - but that usage is nowhere near justifying the price that gold actually trades at.
This is just a nitpick with the use of term "intrinsic value" - gold's characteristics make it a good form of money, but it's still (abstractly speaking) on a fiat basis.
I don't see how it could really work otherwise. There is no such thing as a good that everyone would value equally. Intrinsic value varies depending on the needs of the traders.
See, that's exactly the problem. The intrinsic value of anything - in this case, gold - relies on agreement of the scarcity. Truthfully, we don't know the scarcity of gold, or the amount that exists. We have only educated guesses.
Controlling the monetary supply with "paper" currency (which is an inaccurate term, "digital" currency is the reality) is much more stable and controllable. The US Government says they have $50,000,000,000,000, and the global economic capital markets either agree or don't agree.
This is just a nitpick with the use of term "intrinsic value" - gold's characteristics make it a good form of money, but it's still (abstractly speaking) on a fiat basis.