This would also be quite a bit of overkill. The only akatsuki we know little about are Hidan and Kakuzu. They really didn't have the standard flashbacks of someone who was about to die, but among the akatsuki, they needed it the least.
Hidan is nothing special, really. His only unique quality was his immortality and he know nothing important. And really all we could learn from Kakuzu would have been his battle with the first Hokage. It was assumed that they both survived that battle (because we don't know exactly when it took place), but none the less, that would be important info.
But basically everyone else, Konan, Itachi, Kisame, Sasori, Diedara and Oro are all well covered. Ofc we need to know more about Nagato and Zetsu, but I consider that standard to learn later since they still have a part to play.