The last thing Jaime Lannister did politically was threaten to fling a baby off a tower. With a trebuchet.
The next-to-last thing Jaime Lannister said in A Feast for Crows was how he’d like to tear the tongues out of assorted members of his family: A silent Cersei would be sweet, but I’d miss her tongue when we kissed.
The entire point of Jaime Lannister’s arc is that he thinks of himself as constantly doing objective good, while the world sees him doing objective bad. It’s not a redemption arc, it’s not couched as one if you’re bothering to pay attention to the text.
Cersei Lannister’s arc is a downfall arc, but it’s not Arbitrary Objective Evil brought to heel by a Good and Punitive World: it’s tragically shaped and she brings her own downfall into being by doing what she thinks is necessary to fight for power. (And: fight, yes; maintain, no. Her conception of self-preservation is her blind spot.)
Tyrion Lannister is a better thinker than his siblings, yes: he’s been forced to gain outsider perspective in a way that neither of Tywin’s other two children attained (being especially isolated in twinship, in love, in each other). He’s not privileged within his family in the same way that the twins are, which forces him to seek solace outside of the family—which means making friends in non-Lannister places, but doesn’t mean he won’t murder you with bare hands if you step off his pedestal.
They all try to shape the world in the image that will work out best for them, and they will murder you if you disturb it. It’s a skill they learnt from their father. It’s a legacy they each, all three of them, are perfectly willing to carry out.