If they can make flipping a finger pinch worth of pages somehow doable that would be killer. Some sort of wide-pinch gesture with a semi transparent overlay of the page you are going to flip to with your current pinch width.

A foldable reader with readable panels on each sides when you open it. You can flip pages either way. Pen for annotation if possible. Create/edit your own documents. An icon tap to overlay another document (a note, book page, research paper) so you can add to it or copy from it to the underlying panel.

A reader mode (distraction free) when simply reading. A document mode when you are doing something that requires writing (including simple annotations).

I like books and flipping through them. However if you can blend a book reader with a great note taker that would be ideal.