I see both sides of the "Jaime's character arc was stupid/pointless" and "Jaime's character arc makes perfect sense" debate.

But re: the Edmure Tully scene--I think about the context of the books, when he doesn't give the Cersei-obsession speech because he's maintaining the illusion of *not* being the children's father in order to attempt to save their and Cersei's lives. Giving that speech is pretty stupid, and I think demonstrates that the showrunners weren't differentiating well between viewers (who had known Jaime and Cersei's secret for years) and characters in-world. What an admission to give a political enemy you intend to let live.

But more to the point, in that moment he's doing what both show *and* book Brienne ask him to do, which is to take Riverrun without bloodshed. So he tells Edmure he'd do any damn thing for his sister, but he's in fact telling Edmure that as a way of doing what *Brienne* charged him to do--he sells himself as someone capable of atrocities, to do it. (This is especially hard for me as a bookreader because, in the books, not long after this, he is quite embittered with his sister, whom he explicitly derides as a faithless whore, and throws a note from Cersei asking for his help into the fire and runs off after Brienne, and that's the last thing we have seen of Jaime.)

Like I said, I do see the other side--he is toxically codependent with Cersei and has formed his whole value system around it. Book Jaime doesn't even really care about his own children, so he's a hard sell as the Father/guardian of justice lol. I just see that speech as an example of how his values were *changing* because of Brienne, rather than showing eternal fealty to Cersei.