What exactly is a quantum key distribution network for?
It seems that the initial diagram is correct.  A QKDN is exactly this:-



and it relies on two pieces of kit, a quantum key generator and an encryptor device. A 256 bit AES key is generated and shared between Alice and Bob via the BB84 protocol running over dedicated fibre optic cable. The key itself is created via a true random number generator (perhaps based on the phase interference of a laser beam).

The keys are then passed to the encryptor devices which operate AES between themselves over conventional channels. So actual business data flows only between the encryptor devices, over common networking technology and not the quantum machines. The thing that ensures the security of the transmitted data is that the AES keys only have a life span of one minute.  They're then replaced.  That's why all that quantum data is transmitted.  AES keys are constantly being replaced before anyone could even attempt to break them. Clearly some of the numbers here are dependant on individual networks and hardware.

And QKDNs are used in anger all over the world including government and commerce. The first was deployed in Switzerland to secure their frequent public votes /elections. And there are some interesting future developments that won't require fibre optics at all, and some that will ensure secure key exchange over infinite distances.

All of this is to be found on YouTube.  Don't laugh.  It's a presentation by Kelly Richdale, head of quantum randomness at ID Quantique, a market leader in QKDNs.   There is also an unbiased and fair summary of QKD from  the European Network and Information Security Agency (ENISA) here.  It's concise but rather dated (Nov 2009), so a lot of the open issues should have been resolved or are in the process of being so.