Young Nan

I am aware that it was done as an extortion, but was a confession nonetheless. I agree that the scene was pointless, for all the reasons you said,as was the following one with Jaime. I also hated it because it was totally out of character, Cersei would never do anything to jeopardize her rule through her children. Jaime mentioned it multiple times and she was always against it.

That was basically my take on it. Also, - point for Cersei confessing to Tywin. Jaime was always the one who wanted to do that.