Just to be a party pooper on the whole Charles Dance Party, although I did very much enjoy tywin, I would like to remind everyone of the movie last action hero.
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So he's not perfect.
Having cersie somehow controlling king's landing still, after all her foolishness, is the show's greatest failing. She did so much to piss of the people, who were already shown to be rather fickle. Remember back when Joffrey was king and Cercei was afraid of the peasants? Remember Joffrey was well liked by the people, compared to her.
But she empowers a church cult to take over, destroying all the alcohol, beating up the prostitutes and customers, and enforcing their theocracy. Somehow, the people are OK with this. Then, that church imprisons her, and the walk of shame shows the people fucking hate her. She then has her knight murder a few people at random, her son (The King, remember) publically says she must stand trial instead of a trial by combat, and face justice. Then, she blows up the fucking church, the king is dead (How wouldn't the people assume she killed him?) she's openly fucking her brother, admitting the lannisters were never fucking legitimate contenders for the throne, marrying a pirate king from rape island best known for their ineffective rebellions... and the people are cool with it?
Same thing pretty much with dorne. Now apparently they've got a new prince, after they noticed they no longer had a king. I'm gonna guess the last king's guards are gonna be in a bit of trouble for their lackluster performance...
Also, nobody ever thought of the idea "What if crossbows, but even bigger"? Like, it's just that easy to kill dragons? How the fuck did they conquer westeros the first time? The show should have worked up to that at least, showing qyburn having to overcome some engineering challenges, therefore establishing why nobody ever did this before, and also making them seem less out of fucking nowhere.
Finally.... why the fuck wouldn't cercei just have the archers murder the entire fucking leadership of the opposition while they're idiotically standing at her walls bristling with archers and giant ballistas? This is the one time she's going to be honorable?
The problem is now that everything's so divorced from logical cause and effect we all know literally anything could happen, regardless of how little sense it makes. Internal consistency makes it much easier to accept what's going on.