"With those architectures, a central authority would be required to prevent the double-spend"
Not necessarily; another approach, which is common in protocols that allow offline transactions, is to force cheaters (i.e. people who double spend their tokens) to reveal their identity. It helps to think of the nonce in DSA: if that nonce is used for one signature, the secret key remains secret, but if the nonce is reused in another signature then the two signatures can be used to compute the secret key. Similarly, in a digital cash system, if the same token is used in two different transactions, then the two resulting tokens can be used to compute the identity of the person who spent that token in the two transactions (and hopefully, whoever computes this will warn everyone else about it).
"with those architectures, the coins grow with each spend."
Chaum's result applies to any secure offline electronic transactions, regardless of the internal workings of the transaction. The argument is basically this: to maintain the security of the transactions, the amount of information being transferred per transaction must increase in the number of offline transactions that involved a particular "unit" or its "derived" units (e.g. if the system supports splitting the currency, as Bitcoin does). It does not make a difference whether or not the system has a central authority; all that matters is that the system allows some value to be securely transferred in an offline/peer-to-peer fashion i.e. that a transaction do not require any communication with any parties not involved in the transaction itself.
"The difference with Bitcoin (which I think is totally misnamed) is that it's not a coin architecture, it's a ledger architecture"
I read this as saying basically this: there are no offline transactions in Bitcoin; every transaction involves communicating with other nodes in the Bitcoin network. Which is well-aligned with Chaum's result, because Chaum's result boils down to a trade-off: either you support offline transactions and incur a scalability penalty (which a central authority can fix by trading "old" tokens for "new" tokens), or you only allow online transactions (or something in the middle, like "receipts," which Chaum discussed). I would call the lack of offline transactions a major technical shortcoming of Bitcoin that severely limits its utility, but I suppose not everyone agrees with that statement.
Not necessarily; another approach, which is common in protocols that allow offline transactions, is to force cheaters (i.e. people who double spend their tokens) to reveal their identity. It helps to think of the nonce in DSA: if that nonce is used for one signature, the secret key remains secret, but if the nonce is reused in another signature then the two signatures can be used to compute the secret key. Similarly, in a digital cash system, if the same token is used in two different transactions, then the two resulting tokens can be used to compute the identity of the person who spent that token in the two transactions (and hopefully, whoever computes this will warn everyone else about it).
"with those architectures, the coins grow with each spend."
Chaum's result applies to any secure offline electronic transactions, regardless of the internal workings of the transaction. The argument is basically this: to maintain the security of the transactions, the amount of information being transferred per transaction must increase in the number of offline transactions that involved a particular "unit" or its "derived" units (e.g. if the system supports splitting the currency, as Bitcoin does). It does not make a difference whether or not the system has a central authority; all that matters is that the system allows some value to be securely transferred in an offline/peer-to-peer fashion i.e. that a transaction do not require any communication with any parties not involved in the transaction itself.
"The difference with Bitcoin (which I think is totally misnamed) is that it's not a coin architecture, it's a ledger architecture"
I read this as saying basically this: there are no offline transactions in Bitcoin; every transaction involves communicating with other nodes in the Bitcoin network. Which is well-aligned with Chaum's result, because Chaum's result boils down to a trade-off: either you support offline transactions and incur a scalability penalty (which a central authority can fix by trading "old" tokens for "new" tokens), or you only allow online transactions (or something in the middle, like "receipts," which Chaum discussed). I would call the lack of offline transactions a major technical shortcoming of Bitcoin that severely limits its utility, but I suppose not everyone agrees with that statement.