If 2 wallets are held on the same system
What you are describing sounds like a paypal, or even coinbase. These systems rely on a central party that is in control of the balances for everyone. It's basically just a number in a database and they add "BTC" when it's not actually BTC you are moving around. The number represents BTC but they transfer funds internally or "off-chain". With this additional convenience comes loss of control.
That's pretty much it. It's a separate service that accepts bitcoin as the currency that can be transferred in and out, just as with PayPal. The intention however is to use the "off-chain" nature to allow the use of cards, RFID tags, physical keys etc to allow purchase with an instant payment verification. Instant meaning within a few seconds.
I had briefly seen information about the inputs.io cock up. I would use a 1-way connection to a backend server. Simply sending batch information to the server, and if all data decrypts OK, the server send back an ACK. Same the other way. After a batch, the server will send all updates back, and upon decryption the front-end would send an ACK to the server. Nothing happening in real time, and no way to break into the back-end from the front-end, as the only response that can be sent is either ACK or NAK, and that is just upon decryption of the days transactions ready to be processed by the bitcoin network.
I do understand the anonymity aspect of bitcoin, however ATM's seem to be popping up everywhere, and from what I have seen, they seem to be the most convoluted, and frankly invasive ways of dealing with bitcoin. Government ID, biometrics, payments using bank cards. I'm not wanting to try and change the way everyone uses bitcoin, rather providing an interface for those that see it more as a stable currency, accepted world wide, and not at risk from world financial collapse than an anonymous method of buying things.
I suppose the biggest use case is, supposing this idea works, is well implemented and is adopted by retailers world wide, that you can go anywhere in the world, take your "bitcard" with you and have no exchange rates, no fees for using a card abroad, no trying to work out how much a hotdog is, and having 4096 bit RSA covering your transaction. There is also the security in the bitcoin side of the transaction having a delay, so here is time for disputes to be resolved (or not), before the bitcoin is sent.
The hardware side would remain closed (mostly) and security keys stored on volatile memory along with intrusion detection and self-erasure of crypto keys.
As a system for most of the current bitcoin users, it's utter crap, but I think it may be a help for those that want to be able to accept payments quickly such as retail or fast food, and those that are hungry and can't wait 15 minutes for a double cheeseburger!