Could he turn Apple into an online education platform that leverage open source platforms and open hardware to make it as affordable as possible to everyone? No, he can't. Apple depends on the brand of exclusivity and premium products.
Need I go on?
In any case, it's a sad state of the world when even the CEO of the richest corporation in the world can not be allowed to be interested in anything else that is perfectly aligned with the company's goals.
But anyway, you asked if there is any kind of job that he couldn't do at Apple. I just gave you a couple of examples. You didn't specify that it had to me something that he would be personally interested in doing publicly. I don't know him personally nor I care about him (or Apple) to spend more time and thought about the matter.
But this is getting so much in the realm of the hypotheticals, I really don't care about the argument either way.
If you are already rich enough to retire many times over, why should you keep working on something that doesn't move the scale of your money (and consequently power and ability to do other things, including starting a new business that could disrupt your previous business?)
Think of it this way: a lot of the money that is being paid to Tim Cook is to ensure that he doesn't go to work somewhere else.