My favourite example is that authentic Zimbabwe $100 trillion notes go for >$100 these days on eBay. And I say "authentic," because there's enough of a market that there are forgeries in circulation. (Reproductions are much cheaper, $5-$10.)

Well, theoretically the value of Bitcoin would be a function of energy costs and mining difficulty, but that hasn’t happened in practice, and would still be volatile anyway.

The difficulty and energy cost is a function of price, not the other way around. If the price goes down, miners aren't profitable and some have to quit, which makes the difficulty adjust downwards.

Umm... no.

https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

This says those energy costs are lost to the universe, forever

https://en.wikipedia.org/wiki/Third_law_of_thermodynamics

And this says the underlying value is zero

This is a common misconception. It's the other way around: mining follows the price.

Miners can collectively earn a pre-determined flow of block rewards. If the price rices, then those block rewards become more valuable. So then miners can afford to spend more on hardware and electricity as they compete to get those block rewards.

Now that the price has dropped, the opposite will happen. Miners can no longer spend the same amount on electricity, so many will be shutting down their mining rigs. Only the miners with the lowest electricity cost can keep operating. The difficulty will drop until it is once again in equilibrium with the price.

For real world resource mining, it's different. E.g. if a metal used by industry can't be mined for less than 1 $/kg, then that must put a price floor on the price of that metal (in the long term, ignoring short term price volatility). This dynamic doesn't exist in Bitcoin, which confuses many people.

Yes, in practice mining mostly follows price, but it's still not quite that cut and dry.

Miners also need to sell bitcoin to recoup operational costs. They influence the value of bitcoin by being an active trader and setting limits to their sale price.

Current price influences future mining. Past mining influences current price.

True for Bitcoin. If you want to use applications built on Ethereum, you have to burn ETH, which provides the same sort of demand as for oil.

This can be true if those applications carry some intrinsic value.

However whenever I go down this thought experiment, I tend to find that the applications themselves also don't carry intrinsic value e.g. some tie to the real world outside crypto.

Are there exceptions?

Even if the applications are just weird forms of entertainment, that's still demand that people are paying real-world money for, since they have to spend their real money to buy the ETH. Non-blockchain gaming is a fairly big industry and all the money people spend on in-game purchases doesn't have any more connection to the "real world," but is still valid for financial valuations of the gaming companies.

There are people (especially at EY) working on using Ethereum as infrastructure for things like B2B transactions, but that's still in early stages. And here's a recent piece by Vitalik on non-financial applications of blockchains: https://vitalik.ca/general/2022/06/12/nonfin.html

Yes, plenty of games make money off in-game transactions, and generally they only remain profitable for a few years while they have a large user base, then fade into irrelevance.

But gaming companies can do well for a long time.

Are there any non-speculative ethereum apps? The examples I’ve seen would all be better by just a distributed database with trusted authorities.

The computation and distribution is very expensive, so I’m not sure what I would run on ethereum until transaction costs get down to a penny or something.