Fair enough, but relying upon automatic tellers doesn’t seem to make much sense either. It seems reasonable that the merchants would have had their own means of transferring balances. It also seems plausible, though perhaps not suited to the cataclysm world, that private transactions, lemonade stands, garage sales, drug dealers… Would have some means of transferring currency that doesn’t involve carrying around large quantities of small-denomination cards…
Now, having said that, it would be entirely plausible that the devices used to perform such transactions possessed less internal security than the automatic tellers and therefore would be more reliant upon external communication for verification purposes. With the networks down, the remote devices might not function, but maybe a technically savvy survivor might be able to break into a bank, hook a communications device to the bank’s mainframe, and hack into it to recognise your device as a trusted appliance. Having the bank’s mainframe provide such a service may encourage survivors to refrain from attempting to steal money from the bank’s mainframe due to a risk of the mainframe shutting down and becoming useless. You would probably only be able to steal from a single account per attempt, and there would presumably be no way to completely eliminate the risk of catastrophic failure…
Also, what do I do with my empty cards? I can’t help but think that you could probably stick a dozen of them together and have enough for a unit of electronic scrap and a few plastic chunks… You know, we really need microwaves, I want to just dump all my empty cards into a microwave and see what happens…