How much "intrinsic value" does gold have and how much "the greater fool/scarcity" value does it have? Of the $4,080 spot price for gold, maybe a few hundred dollars could fairly be attributed to the industrial, cosmetic or medicinal "intrinsic value". The vast majority of that $4,080 price is attributable to the exact same thing that the $86k bitcoin price is attributable to -- that someone else thinks the scarce asset is worth that price.
The fact that bitcoin has no value separate and apart from demand does not really seem significant to me when so many assets are primarily valued based on what other people are willing to pay for them (as opposed to discounted cash flow of present value of future income).
1. I am not trying to divide assets' valuation into intrinsic value and greater fool value. That's not possible, as you note. For one thing, for many assets, the intrinsic value is a function of expected future returns that are highly uncertain. So it's impossible to distinguish someone paying $400 for a TSLA share because they think a greater fool will buy it, versus someone who merely thinks that TSLA is going to make astronomical amounts of money over the next decade.
2. The distinction is between things that have no value and things that do. It's pretty safe to say that bitcoin is not valued by its stream of future earnings as it has none. It's not as if people are saying, "I expect the bitcoin ROE to be 12% on a forward going basis" or "no, it's only going to be 9%." There's no ROE at all.
3. If you're arguing for crypto, then yes gold is your best analogy. To be honest, I find gold's valuation to be something of a mystery. But in any event, gold is fundamentally different than bitcoin for two reasons. First, it has been the basis for monetary systems for thousands of years. That has given it a "special status" in finance, perhaps like baseball in antitrust. Second, and more importantly, central banks all over the world hold gold. They are, in many cases, required to by law (I think that's true in the US but I'm not going to look it up). A lot of the demand for gold comes from central banks. So while the government doesn't fix the value of gold as it does a fiat currency, it is still shaping demand by law, which is a form of establishing value.
So again, the difference is between government-created valuations (dollars and gold), and pure market froth (crypto). This is why the crypto folks are trying to get legislation passed in many places that would require banks to hold "assets" in the form of crypto.