Many say that fiat money in its physical version is fungible, but it is not always so.
For example, would you accept a badly deteriorated bill even if you verify that it is legitimate?
Not all banknotes are fungible.
Discussion
But you would be able to exchange this note for a new one at the bank so I would consider this as fungible.
Of course, you go to a centralized intermediary by removing the p2p action.
That's exactly what happens in crypto space, most use custodianship and intermediation rather than self-custody and p2p.
It is a matter of concept and philosophy.
You’re comparing the fungibility of fiat banknotes (which relies on a central authority for their issuance) to Bitcoin. Actually with Bitcoin, it is the intermediaries that degrade the fungibility of Bitcoin.
Not only that but the bills are serialized for the express purpose of being individually identifiable. Literally not fungible.