"Three words: bank shuts down"

It is not as though cryptographers gave no thought at all to the single point of failure in digital cash:

http://cs.brown.edu/~anna/papers/lr98.ps

You can set things up so that it would take the failure of the entire banking system to destroy your cash, which is not different than the failure of all Bitcoin exchanges. This is still neatly aligned with the modern understanding of fiat currency; you can have multiple banks that are responsible for issuing currency and accepting deposits.

It is also important to recognize that while a bank failure would be fatal to a digital cash system, a "51% attack" on Bitcoin would not be fatal to Bitcoin (the system allows such attacks as part of its design). The attack could be selective, it could be disguised as a "block chain fork," etc. Equally important is that the "51% attack" can be performed by any party -- it requires no secret knowledge or special privileges. As bad as a single point of failure may sound, the bank is a clear point of failure and it is not unreasonable to imagine taking special precautions to protect the bank from failure (or to reimburse the bank's customers e.g. FDIC). No special measures can protect Bitcoin users from one party doing a lot of computation and invalidating / reversing / denying transactions, something that is inherent in the design of Bitcoin.

"Actually there is, but that requirement is concentrated in the bank, which all users have to trust to steward the currency's value"

I had said identity authority, not currency authority. Look at Chaum's online protocol again, and find the place where an authority on identities is required. The bank is the only party in the system that requires a signing key.

Offline protocols are different, but that is beyond the scope of any conversation about Bitcoin. Bitcoin is an inherently online protocol: every transaction requires a connection to the Bitcoin network.

"your definitions preclude the novel and necessary parts of Bitcoin"

I think you have that backwards. Chartalism and modern monetary theory (which forms the basis for fiat money) predate Bitcoin by decades. The security definitions used in provably secure digital cash systems predate Bitcoin as well. Bitcoin's own design makes it incompatible with those previous definitions.

There is nothing wrong with rejecting the existing definitions if you find that they fail to capture some important property, but if you choose that route you need to present a novel definition. That is exactly what you see in the work on offline digital cash: the security definition used for online protocols is too restrictive, so a different definition is used (i.e. it is possible to cheat but the identity of a cheater must be revealed). Unfortunately the Bitcoin community has yet to present a novel security definition or a novel definition of money, or at least they have failed to present satisfactory definitions. Again, what is the definition of "valid" money in Bitcoin? What is the definition of "security" for Bitcoin?

"If exchange A calls coins stolen and refuses to exchange them, exchange B will still exchange them because it hasn't become aware of this yet, and less-reputable exchange C will exchange them at a 50% discount, are they "valid" ?"

This is a case-in-point. There is no definition of "validity" for Bitcoin money, so there is no answer to that question. I am not saying it is easy to formulate a good definition. What I am saying is that such a definition is necessary, at least as far as cryptography is concerned.