The cryptocurrencies that "fix" this problem vary in the cryptographic tricks they use, but it all boils down to drafting everyone to act as fences as a condition of partaking in the system at all.
It's a technical solution to a social problem. It won't work. You can always move value in, but out is another matter. Trading your Monero (or whatever) for legal-economy assets or currency may be criminalized any day.
> it all boils down to drafting everyone to act as fences as a condition of partaking in the system at all
Indeed. Monero uses ring signatures: every transaction is signed by 11 users and it's impossible to know which signature was responsible for the transfer.
No. Oil is fungible too - any barrel of a given grade is treated the same any other - but that doesn't mean oil buyers and sellers are fences for each other.
What you're thinking of is the "current" aspect of currency. That when I take payment for a bagel in my shop, I don't need to worry that the money used to pay me was stolen, I still get to keep it.
But this is a social, legal concept, not a technological one. Calling it a currency won't make it current. Fungibility doesn't make anything current either (if I was stupid enough to take payment for a bagel with a barrel of oil, I WOULD have to return it if it turned out it was stolen. I should have known there was something fishy!). No amount of cryptographic cleverness can force society to treat it as current.
I'm pretty sure cash falls into the "stolen goods" category, and you don't get to keep them even if you didn't know they were stolen. You'd have to give the bagel cash back just as much as the barrel of oil.
(Well, in my jurisdiction. Source: family member is a lawyer)
Traditionally, you wouldn't have to, though - that's why they called it "currency", because it is "current".
I believe it still works that way for bagel-level money in most parts of the world. If it's higher amounts, I'm not sure - you certainly have a lot of due diligence obligations, and if you didn't do them you certainly lose it (and you will be in trouble, too).
The roots of the word currency do not stem from your sense of "current", by which you seems to mean something like "immediate".
It primarily comes from the Latin currens which means to run, or flow.
It's monetary sense comes from that, as money can be thought of as flowing throughout the economic system. The temporal sense of "current" comes into play only as denoting something like "the present day medium of exchange" not "immediate". Bank notes and checks for example are both forms of currency but are not immediate.
The immediacy of cash-- separate from its status as a currency-- does not confer it special rights. To use something less trivial than a bagel, think of a car. If the dealership is notified that it received stolen cash for a car, it now knows that it is in possession of stolen money. It cannot legally keep money it knows was stolen. The exchange it entered into with the thief was itself not a legal transaction. The cash goes back to the rightful owner, the dealership gets to fight it out with their insurance company to get its own money back.
No, that's a consequence of fungibility in the context of some privacy uses, not its definition. The definition of fungible items is that you can mix them without altering their properties.
Fungible items can be used as a commodity, for instance: if two people buy cereals, they may use the same silo to spare on warehousing costs.
Fungibility is always true within a limited context, though. Examples of failed fungibility include Amazon comingling genuine products with fakes, or, to draw from the previous example, cereals from different areas will likely have different gluten or humidity rates, and while producers from an area may share a silo, the buyer may keep the same cereal from different geographic areas separated. Another example is electricity, with power being fungible in terms of who puts it in, but absolutely not when it comes to when power is provided.
That's a pretty good example of introducing artificial fungibility "to spare on warehousing costs". It goes without saying that this also leads to risk for customers; there's no way of knowing if an order for some given SKU will be fulfilled by a genuine product or a fake. It's nonetheless true that you can arbitrarily mix orders without changing their fulfillment properties, so a kind of fungibility is indeed present.
It's a technical solution to a social problem. It won't work. You can always move value in, but out is another matter. Trading your Monero (or whatever) for legal-economy assets or currency may be criminalized any day.