You simply can't get anonymity without cryptography.
I think your mixing anonymity, privacy, fungibility and encryption.
No but you are conflating them...
Four very different things which have potentially nothing to do with each other and which are optimally deployed in very different use cases.
Anonymity basically alludes to anything that doesn't have a name attached to it.
Correct. Well summarized.
Where the medium is perfectly visible but where any association with individuals has to be gleaned from outside of that medium. For example, if I receive an anonymous message from some woman telling me that she loves me then the message is perfectly visible, it just doesn't have her name on it. I have to start doing research outside of the realm of valentine cards to find out who sent it. I can show the card to all and sundry and it's still anonymous.
Conflation. It may very well be that to protect her anonymity it is also necessary to encrypt the message for one reason or another, e.g. writing style correlation or other meta-data correlation. Anonymity always requires at least some privacy, e.g. her name was also elided or encrypted, else she'd not be anonymous.
Privacy, on the other hand alludes to a restricted audience. For example if someone goes to the crapper and locks the door, they'll be the only individual partaking of the experience. If you make a bank transaction, only you and the bank staff will be privy to it.
Correct. Well summarized.
In neither of these cases, though are you "anonymous".
Slight implied conflation. Privacy doesn't require being non-anonymous to those who you don't grant access to your data. But you are correct that privacy is orthogonal to anonymity. A good example is encrypted email could be private but from the IP address and meta-data, it isn't very anonymous.
Encryption is one method of enforcing a restricted audience - i.e. privacy. It does not, however, make you anonymous.
Encryption can indeed make you anonymous, but it doesn't have to. What do you think Cryptonote is? It is encrypting the UTXO payer (but not the IP address or other meta-data correlations).
Fungibility is a property of a (monetary) medium which makes 1 unit of that medium indistinguishable from another unit. Fungibility does not necessarily enforce privacy because it doesn't "hide" anything. But it does mitigate the propensity to discover the historical movements of a unit of that medium. Fungibility therefore DOES boost anonymity in a way that encryption doesn't.
If my anonymous admirer sent me a totally fungible valentines card that was printed with nothing but I LOVE YOU on white card, and all other valentines cards in the world were exactly the same, I'd have a damn site harder time tracing her than if it was handwritten fluorescent pen that was only available in one shop in my local town. Either way, no recourse to encryption is needed. Nor is it with regular cash, precious metals or any other monetary media that have been floating around for centuries, serving as the reference standard for monetary anonymity.
Seems you are conflating fungibility with the state of being elided. Fungibility has to do with being substitutable. If elided information is what makes fungibility, then vacuous would be the ultimate fungibility which makes no sense because fungible items have to existential.
Hey i am getting sleepy. Too many hours of discussions again. I really need to stop this. But even sleepy, you are not going to get away with lapses in logic in spite of being very articulate. You are smart, but I am not stupid.