It's value is inherited from the same basis that gives fiat currency its value, which is to say, pure magical thought.
Completely untrue. flat currency gets its value in that it is backed by the government and economy of a nation state.
To be more precise, it's backed by the enforceability of debt contracts, i.e. the judicial and executive branches of the nation state. But that's only what makes sure the value is provided, what actually backs fiat currency is someone's legally-binding promise to do some sort of productive work. Fiat money is created by banks when they issue loans (including but definitely not limited to the Federal Reserve bank), so every dollar created is balanced by a dollar of debt that is created at the same time, and when the debt is paid off, the dollar ceases to exist.
Suppose you want to build a new house. You go to the bank and borrow, say, $1M. Many people think the bank loans you $1M that they have sitting in their (virtual) vault, money that was deposited by people with savings accounts at the bank, but that's not true. What happens is that the bank invents $1M to lend to you. It's not quite that simple (but note that we've abandoned fractional reserve lending; there are no reserve requirements any more), but we'll gloss over the irrelevant complexities. The core point is, the bank creates (a) $1M and (b) a mortgage contract, which offset one another. $1M came into existence, but there's a promise to repay, and therefore destroy, that money.
You pay the money to the construction company, who pays it to their workers and suppliers and investors, and they build you a house. You move in and all is good, except now you have an obligation to apply your labor for the next 30 years to generate value so you can make your monthly mortgage payments.
That is what backs fiat currency: The future labor of borrowers. The exact nature of the labor is undefined, of course, but that doesn't make the labor itself any less of a very real, very productive (by definition!) asset, and it is that productive asset that gives the currency its intrinsic value. And, of course, the legal system is backing the contracts, so you can't just decide you don't want to pay, not without significant negative consequences. That's just one of a number of crucial roles the government plays. Another is the laws that mandate that all debts public and private be denominated in and payable with the nation's currency.
Obviously, crypto assets (they really aren't currencies; even ignoring their lack of intrinsic value, they suck as currencies) have nothing remotely comparable to that sort of solid foundation. Less obviously, so-called "hard" currencies don't either. The classic hard currency, gold, does have a little intrinsic value because it's pretty and has some useful physical properties, but the vast majority of its value is "pure magical thought". It has that value only because everyone believes it does, but there's nothing behind that belief but tradition, not even anything as abstract as contractual obligations. Unlike fiat currencies.
