I've considered a strategy of buying gold post-collapse on the grounds that on the 30-year business cycle, gold will probably be spiking again in the next financial crisis at right about the time I'd be retiring, but that's 100% pure speculation, not buying for "intrinsic" value... but then, I scare quote the term since there really is no such thing.
I also think investing in gold in the case of total collapse is a bit bizarre, because in the event society totally collapses, the only gold that will be worth anything is the stuff in your physical possession, not numbers in your bank account, which the government trivially confiscated (shortly before it discovered that doesn't prevent collapse either, because the government's problem was never having enough numbers in computers). (They can confiscate physical gold too, of course, it's just not trivial.) I know that's not the motivation of every gold bug, though.
Currency at its most basic level is a representation of the value generated by the society it is used in. So the number of U.S. dollars represents the entire value of what U.S. citizens produce at any given time.
What makes commodities valuable as currency is they are finite. There's only so much Gold, Silver, and Bitcoins in the world. Since all these commodities can be used as currencies (i.e. they can be converted to paper currency) they represent value beyond just its practicality because it stays consistent as the amount of each fiat currency available grows.
So Gold goes up in value because it isn't really going up in value. Everything else is going down.
That's not even close to correct under any theory of economics, I don't even know where to start explaining that.
"What makes commodities valuable as currency is they are finite."
No, that just means they happen to exist in the real universe, in which everything is finite, which is hardly a way of distinguishing between "currency" and "not currency" (in information theory terms, that has no information in it). What makes currencies valuable, and what makes things valuable in general, is that people want them. People want the government not to smash their doors down and haul them away and put them in jail, or freeze their assets, etc. The rest of the value of a dollar recursively emanates out from that. There's a value to having a dollar beyond just the goods and services that can be obtained, it prevents Uncle Sam from destroying you. There's no value to a BitCoin; the base case of BitCoin is "zero", unlike a dollar or any other government fiat currency, unlike gold (which has industrial and decorative uses which may not stay constant but won't drop to zero for a long time), unlike anything else called a "currency". Currencies aren't arbitrary numbers.
(Not being jailed/fined/killed by something may seem like a bizarre base for a currency if you think about it, and I wouldn't disagree. I do rather wish people understood the gravity of treating "government" like a silver bullet and just firing it every which way to solve every problem, especially when turning everything into a criminal law offense. However genteel we've made it over the centuries, it's still pointing guns at people, and I'd prefer to reserve that for truly important things.)
Gold is still valuable as a medium of exchange largely due to historical reasons but the problems of moving gold, storing gold and using gold for very small transactions outweigh its benefits for anything other than a store of value, gold is simply too crippled to be used as a currency.
Bitcoin aims to fill that gap by having similar properties to other successful stores of value, (durability, reasonable finiteness) along with medium of exchange properties like fungibility, but at the same time being digital and thus adding properties like near instant transfers (on a global scale) and near infinite divisibility.
Its not certain if Bitcoin will be successful, something better might turn up to replace it, but IMO a purely digital currency definitely has a future.
So, how about if someone would get a farm of computers mining bitcoins, at a rate where the bitcoins pay for the electricity etc, but then they also rent out this computing power for anyone to use for whatever purpose (like Amazon), but for this accept payment only in bitcoins, being the exact amount of bitcoin that would have been mined otherwise with the computing power rented out.
Would that work?
Then you back it with something else of value, namely computing power, but you only accept bitcoin as payment.
Just a thought, though.
There's at least two major problems with your particular proposed backing: Computation power isn't actually worth that much, and the value of a given amount of computation power is sinking fast, and will continue to do so for the forseeable future. This creates practical problems in providing enough backing to power an economy. And a couple of "bonus problems": Allowing people to perform arbitrary computations on your hardware can have certain legal problems, and the process of solving this problem may raise nontrivial overhead. Backing your currency with a service rather than a good has interesting implications in a "run" situation because you've added an unavoidable temporal component to the process of cashing out the currency, which is the sort of thing you could probably squeeze a PhD thesis out of describing the precise effects of that, but I doubt they're very good. But at least it would provide a non-zero backstop to the currency, which would be a start.
(Interestingly, if we ever hit a final equilibrium on the price of computational power, note my two major objections go away. While some practical problems remain, one could imagine the rest could be worked out. Could a computation-backed BitCoin variant be what powers Economy 2.0 in Stross' Accelerando?)
But what happens if you do business entirely with an unofficial currency like BitCoin, do you have to pay taxes based on some arbitrarily converted USD value? Or can you escape taxes altogether?
When you win A New Car! on the Price is Right, you better believe the IRS and all relevant local tax municipalities express no confusion on how to tax you for it. BitCoin would not be particularly different. Without a rigid wall completely separating the BitCoin economy from the greater global economy (in which the USD is only one player), the greater global economy will tend to efficiently price a BitCoin. ("Efficiently price" is a technical term, what it means in this case is that the conversion rate in some sense has a real existence and isn't just a polite fiction, though there's a couple of simple logical steps betwixt the raw definition and that conclusion.)
There is basically no escape from taxes, other than any that may be explicitly laid out in tax law.
This is why a government is so tied to its currency. In some sense it isn't a true cause and effect relationship, both the stability of a government and the stability of its currency is tied to the same third factor, its credibility.
"All a currency really needs to be valuable are two people who have faith in it"
Which is an equivocation game, in that "have faith in it" must itself be motivated by something at least locally rational or it won't work. I have faith in the ability of a dollar to buy off the men-with-guns who will come and take all my stuff and ruin my life if I don't pay my taxes.
All government fiat currencies are thus in fact backed by something real. I don't entirely disagree with the BitCoin community that that is a more tenuous backing than one might abstractly like, but I do not see anything in practice that would be better; value stores are intrinsically ephemeral and there is nothing you can do about it.
The reason why BitCoin is crashing is that it was built on the false premise that currencies have no backing, so we might as well create a cryptocurrency with no backing. But that's false. BitCoin is actually special in having no backing of any kind, and that is why failure is and will continue to be inevitable. The whole thing was built on a false foundation.