One major explanation for why cryptocurrencies can maintain a price without relying on burning coins from transaction fee revenue is the “store of value” argument. The value of the token, the argument goes, comes from nothing more than the fact that people can use this token in order to store their wealth, and so the price is backed purely by a self-supporting inductive argument: people see that the token had value from genesis until T-1, that is currently has value at time T, and so it will very likely have time at T+1 as well, and because of this expectation people buy (or refrain from selling) the token, causing the prophecy to come true.
Theoretically speaking, this is NOT the same thing as saying that a cryptocurrency is a bubble, because unlike bubbles the argument I describe is stable under rational expectations - that is, it does not strictly speaking depend on any of its participants to be irrational or deluded or have incorrect opinions - whereas a bubble does (hence phrases like “bagholder” and “greater fool theory”).
All that we need for this argument to work is an equilibrium where the cryptocurrency grows at the same rate as the global economy (or possibly even at a slightly lower rate), and where it has properties that make it useful to hold in some quantities (particularly, having risks uncorrelated from risks of stocks, making it useful for diversification, and security properties, one of which is censorship resistance).
Even the latter by itself is valuable; to some extent one can view a blockchain as being like a security company which keeps gold safe (though only against some kinds of risks!) and which charges some percentage fee per annum that makes up its revenue and from which is derived its market cap, except where the asset held by the security company is the shares of the company itself.
Now, we get to the next question: which cryptocurrencies get to have this special store-of-value status and which ones do not? Clearly, it’s not the case that just about anyone can fork the Bitcoin code on github, publish the coin, and expect the market to assign it a value, not to mention a value remotely close to bitcoin itself.
Theoretically, there is an infinite number of possible equilibria: just Bitcoin has value, just Bitcoin Cash has value, just Bitcoin and Ethereum, just IOTA, just those in the current top 1000 on coinmarketcap where the sha256 of the listed name is a prime number, etc. But there are also equilibria where the set of cryptocurrencies with nonzero value is not fixed, and new cryptocurrencies can join. However, if just about any cryptocurrency can join the club, then there is a problem: everyone will want to make cryptocurrencies to sell tokens and make a profit, and so the price of all of the cryptocurrencies will crash to zero (or at least to their underlying use value, something based on future expected discounted transaction fees). So is there some equilbrium in the middle?
The answer is yes. Consider a scenario where there is a set of entrepreneurs, and entrepreneurs can expend capital to create a “signal” associated with their coin. Expending $M of capital creates a signal of strength M * R(), where R() is a random distribution with mean 1. The equilibrium is simple: a cryptocurrency with signal strength M is valued at an initial market cap of M * k, where k decreases as the total market cap of all cryptocurrencies as a portion of global wealth increases (additionally, we need k > 1 where there are no cryptocurrencies, and k < 1 where cryptocurrencies make up 100% of all global wealth).
The total market cap of all cryptocurrencies at any point in time is at the point where k is slightly above 1, so being an entrepreneur is in expectation slightly profitable. If world GDP increases, say, 3% per year, then one could imagine that existing cryptocurrencies on average increase 2% per year and every year some new cryptocurrencies appear with total initial value on average equal to 1% of the value of the existing cryptocurrencies. This is a totally long-term-stable situation; the market share of cryptocurrencies as assets remains long-run constant.
Now we can ask, what is the signalling that entrepreneurs are expending capital on? Theoretically, it could be anything. Even if each cryptocurrency developer signals by building sand pyramids in Egypt, and people want to purchase the cryptocurrency with the most impressive-looking pyramids, the model still works. However, in practice human beings want at least the pretense of not doing something completely ridiculous, and there are informational obstacles to people learning about cryptocurrencies, so the signalling activity comes in two primary forms: (i) technical development, and (ii) marketing, with marketing taking up an increasing share (including social media marketing, public billboards, as well as expenses such as paying up to $1-15 million dollar listing fees to major exchanges). In order to enter the club of cryptocurrencies that benefit from the “store of value” position, an entrepreneur need only do enough tech development and do enough marketing to build up a community to be seen as worthy.
This shows how even a free-entry market of issuance of intrinsically useless digital assets does not necessarily need to lead to all of the assets dropping to zero in the long run, if a separating equilibrium based on signalling expenditure emerges (and I would claim there’s a good chance that this is in part what’s happening now). Issuing new currencies is nearly free, but issuing new currencies that people care about requires an increasing amount of “marketing as proof of work”.
The alternative story for cryptocurrency valuation, and one that feels less spooky to friends of classical economics, is the one I describe here: cryptocurrencies are like corporations, where their valuations represent the expected future discounted sum of coins burned from transaction fees. Currently, very few blockchains satisfy this property; although Bitcoin’s fees have at one point reached $20 million per day, corresponding to a quite reasonable-looking “P/E ratio” of ~30, and Ethereum has reached about a fifth of that (though fees on both chains have dropped now, to $600k/day for BTC and $550k/day for ETH), fees can only be viewed as revenue; the fees are paid directly to miners, which to the blockchain are security expenditure; there is no profit left over.
In pure proof of stake, even if no coins are burned, a weaker version of the model still exists: a coin is a tool that you can use, with some further effort, to get a share of transaction fees; it is like a virtual mining pick. As long as the effort is less than the reward, the tool takes its share of the difference as its value.
Theoretically, a cryptocurrency world where cryptocurrencies are primarily valued as shares of future burned transaction fees, or as tools that can be used to access transaction fee revenues, is a much healthier one; putting aside outright scamming or tricking people, the only way to earn money is to build (or, by holding tokens, financially support) a blockchain that people actually use.
Given that P/E ratios less than 100 are demonstrably within reach (compare: in 2009 the S&P had a ratio of over 120), getting to this state is quite possible. And in fact, even in the current environment it should be the case that coins that get a large amount of actual usage get an advantage over coins that do not. The reason is simple: suppose that all cryptocurrencies are going up an average of 2% annually, but then one of these cryptocurrencies burns 0.5% of its coins annually from transaction fees. That cryptocurrency will go up an average of 2.5% annually, and so in a portfolio theory model it will be more attractive to hold larger quantities of it. Hence, in the long run we do expect the best stores of value to be things that are useful for other reasons first, and stores of value second.
That said, it is worth noting that in the current market, where cryptocurrencies rise and fall by over 10x annually, the difference between 2% and 2.5% expected annual growth is virtually impossible to see; hence, it may take some time for an equilibrium different from the current one to emerge.