Every asset class does. USD has the US military, gold has difficulty of mining, crypto has maths, watches have complexity of their construction and are a lightweight store of value, art has emotional resonance.
Difficulty of mining is a supply side constraint.it doesn't give gold its value.
Gold has long been prized because it doesn't corrode, and makes nice jewelry. There's also industrial applications.
Who admires the maths of their bitcoin? They don't, it's just a supply constraint. Constraining the supply of something that has no value doesn't make it worth something though.
Likewise you probably need a military to defend your country from those who might invade and replace the currency, but that doesn't impart value.
Aluminum used to be more valuable than gold. Then we discovered cheaper ways of processing the ore. Aluminum is so cheap now that people throw away aluminum cans everyday (hopefully in the recycling bin)
People rarely throw away gold like that although some does get tossed in electronic devices. If we found a way to decrease the cost of gold mining by 1000X then maybe people would throw it away like aluminum.
If you have one thing then the price should be whatever the highest bidder is willing to pay, if you have a million things, it's whatever the the millionth highest bidder is willing to pay. Thus the more of a thing you make, the less valuable each thing is. This works, because the total value of $things sold increases.
But that 1, or those million people buying the thing have to be willing to pay something.
An aol disc isn't worth anything, even now that they are probably exceedingly rare (I'll bet someone's flogging them on ebay though) because still no one wants them.
Aluminium and gold have fundamentals because they have a use. Some random coin, not so much, not even as a coaster.
And a base value of zero is way different from any positive value, in so far as it can drop 90% an infinite number of times, but something with some use aside from exchange will drop only till it hits the market price of that use.
You folks are arguing past each other. As it turns out, the price of something is determined by two factors: Supply and Demand. Imbalances in supply and demand cause changes in price.
Scarcity is a major part of gold's value. Gold's value comes from being scarce and easily divisible. It means I can pay for something in an exact small bit of gold.
It doesn't have to be useful or pretty to do either of those things. That's the case for bitcoin being digital gold.
The problem with bitcoin is that it isn't significantly better than gold at doing either of those things, and obviously isn't any better than any other random unit in another distributed crypto ledger. You can create new crypto tokens so fast that people went from trading particular to issuing single instances of new tokens with NFTs.
Being useful and pretty just provides a baseline value; gold is never going to fall to zero. But the important part is that nobody is about to invent a new gold to compete with the old gold on the merits of scarcity and divisibility. Even though bitcoin when considered alone is a nice try, every other cryptocoin destroys its scarcity.
I'm not sure if you're conflating value and worth or missing my point.
If there was only 1 Oz of gold and Mr X was willing to pay $1bn for it. Gold would be worth $1bn. But there's more than one ounce and the market clearing price is much lower than that. Mr X may still value an ounce $1bn, but he doesn't have to pay that, he gets a relative bargain. If no-one valued gold at $1 an ounce today, you shouldn't be willing to pay $1 if there was only 1oz.
Supply just creams of the top people who value gold most highly. Scarcity just means you're creaming off a smaller higher valuing population.
So scarcity doesn't give something value per se.
Id agree in certain edge cases that scarcity does increase value. I'm not sure if gold is an example of not. There are other rarer elements that don't have the same cachet. But in general I don't think scarcity itself adds value.