Well, the logic of inspiration comes from Dieter Rams' design of the Braun T3 radio (see image below).
It is well known that Apple's chief designer Jonathan Ive "borrowed" a lot of inspiration from Dieter Rams' designs for Braun (although this particular one is attributed to Phil Schiller).
In fact, this is a recurring question at any event or in any article where Dieter Rams has a say (and he's very happy about it, no problem at all, he even says that Apple has improved on his vision)
Other than aesthetics, it was not particularly intuitive, at least no more intuitive than putting all commands together in a row like any other device.
As for why, I know of two theories (which could be combined), though I am not sure they are true:
- One is that it was just a tribute to Dieter Rams.
- The other is that they needed the space for the electronic circuitry inside, and that the user interface either had to have empty space or fill that space with the screen or controls. Since the controls were (are) much cheaper than the screen, the UI design came to the rescue and they used this large dial that made it iconic and elegant.
As for why it was discontinued, recent iPods have been equipped with touchscreens because they offer more features and screens are cheaper these days. iPods have not had mechanical controls since the iPod Nano 5th Generation in 2009.