It won't happen. This isn't to say there won't be other private digital currencies in the future but it makes no sense to have a blockchain.
Thanks - this is exactly what I was hoping for (a well thought out response).
Why exactly would banks not agree to a "decentralized" system if it is in their own advantage (reputation per GFC in my OP)?
As a hypothetical lets say a one of the banks got hacked and attackers used their mining node to implement a billion dollars in double spends. Are the banks going to let that stand? Of course not. They are going to reverse those transactions (roll them back). How can they do that? Simple it is a centralized network. It would be no different than a PayPal reversal or credit card chargeback. So mining does secure this "bankcoin" network the centralized control does. If mining has no purpose then there is no reason to waste the resources doing it.
I understand that the whole idea of "mining' would be very new to any existing bank, however, with the idea that mining can only be done by permitted IP addresses stops the problem you are referring to - doesn't it?