I loved the episode. I think some of y'all are missing some things. Character arcs arent necessarily about change. None of these characters have changed in who they are. They may have grown, but that doesn't mean change. This episode makes sense.
Everyone always feared that Dany would burn the city, when they learned she had 3 living dragons. She was groomed into a savage from the beginning. And any time she got upset, she burned people. She got the Unsullied by robbing the plug. Tyrion, Varys, were there to set her on the diplomatic path. They failed. She only knew one way. That was never gonna change.
Tyrion loves his siblings, especially Jamie. Lannisters are bluffers...except Joffrey. Even Tywin said he was never gonna let them execute Tyrion. Jamie did everything for Cersei. Cersei said "we belong together. We came in this world together. We're leaving together." Tyrion was gonna do what he could to save his family.
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The "not making sense" thing is much more about the whys and hows than the whats of the story.
Dany burned and killed people that betrayed her, opposed her or stood in her way of being a good/different kind of ruler she was never a mass murderer nor felt compelled to kill innocent people. She showed mercy from Season 1 when the Dothraki were raping and destroying towns and even got in trouble for that. I would buy her becoming mad like her father if HOW she got there made more sense. I'm pretty sure GRMM's idea is to make her go crazy too. But this was so plot driven that if felt forced as hell. Varys and Tyrion didn't fail to reign her in, they were the MAIN reason everything went to shyt and her life was in shambles.
We just saw how destructive Drogon is. From day 1 Dany wanted to go to King's Landing, burn the Red Keep and get rid of Cercei. Now we know that would've taken her 10 minutes. The show made it a thing to destroy Tyrion's intelligence by making him take retarded decision after retarded decision just so Dany's forces would get depleted and we could feel there was a level playing field between her and Cercei...turns out that none of that even mattered because Drogon obliterated the entire city with the quickness anyways
Tyrion NEVER loved Cercei, he only cared for Jaime because he was good to him when nobody else was. He despised her sister, over and over again. He promised her he would hurt her if he had the chance. But when the story needed him to stop Dany, Tyrion had to trust Cercei a bunch of times and be made a fool. Now not only that happens, but now we have to believe he cares for her to live to the point of sending Jamie to rescue her?
Tyrion didn't give a single fukk about his family when he killed his fukking father for being an a$$hole to him and fukking his girl but he's all about family now?