Jony Ive had been the CDO for years and the results weren't great. It's not that Jony Ive isn't a great designer. It's just that it's difficult to judge your own work, no matter how good you are.
What they need, more than a CDO, is someone who they have to run every design by, someone (EDIT: with an impeccable eye) who is not afraid to say no. In other words, someone who can fill the role Steve Jobs used to play.
I, for one, nominate the great John Siracusa, for this job.
Without knowing Apple internally, the point is that the staff under the COO (if the "C"s have their own divisions) are the back office, the accounting, HR, IT, and other shared services accross an organization. There isn't necessarily creativity as a mission.
Cook doesn't (and recognizes that he doesn't) have the necessary design eye.
I think I agree with @UIZealot that there's a need for a design approval that isn't directly involved in the design process, e.g. the SJ world would presumably have SJ saying yes/no to Jony, but in the post-SJ world it was Jony saying yes/no to essentially just Jony. I assume those decisions would be fairly one sided :D
Cook would've been perfect if he had that critical eye, and he would've been the perfect replacement for Steve Jobs then. Alas, he's an operations guy, design is not really his forte. And that, my friend, is the reason we are in this nine circle of flat design hell.
I can imagine that there is actually nobody who wants to be the new CDO. I mean.. you would have to take over the design lead for the world's most valuable company. Also take over what I've created and build up on this. But also be prepared to be talked down by existing folks at Apple to follow their expectations, like "you have no clue what we really need".
Someone with great bravery and mental strength would be needed here.
I am not that into design at all so excuse my question: is there someone who would probably be the perfect fit for this position, at least design-wise?
I sort of agree and disagree with it. I think they need someone like jobs with design taste and product / user focus in mind. More like a Chief Product Officer.