This must surely be the next step for Bitcoin and digital currencies - and for that matter fiat currencies too.
How would this be implemented? I could imagine maybe something like this:
A separate blockchain network with an IBAN/BIC id which maintains the bank account records for the participants. Each account would effectively contain the public addresses that the account owner wants to include - effectively links to the Bitcoin blockchain.
To activate transactions with these addresses requires the private key for the respective public address/es. These would be stored encrypted at the client end, together with a private key and additional security procedures for the account
Interfaces or gateways to the other blockchain networks and the SWIFT banking network would also be required - maybe built into each node to provide for redundancy and full reliability. Or perhaps provided by a tertiary level run by businesses as a service.
This system has the advantage of keeping all your transactions and balance information in one place, not spread out over different addresses. Its a step beyond a wallet, since the owner uses just a single bank account number for sending and receiving money.
Transactions could be in any currency, Bitcoin, Litecoin, Dash, etc, and to/from fiat currencies provided that there were interfaces to exchanges and automatic conversion. This could be configured via the client end.
The client-end access would be client software/app similar to the present with wallet software, or via web-based services provided as a business with paid for premium services and basic level access maybe free of charge like with email today.
The idea is to take Bitcoin and other digital currencies one step further and create real peer to peer banking with no intermediaries, faster, and at much lower cost to the consumer.
Next question: is it viable right now - and if so, how can it be implemented?
This is possible if there is a big company that will buy bitcoin in huge amount and store it. Then they can just create an offline digital numbers that correspond to the actual number of bitcoins at their storage. The bitcoin will backed up their digital numbers or money and those digital money will be used by users even in offline transactions.