"Why doesn't Dany go mad? Why doesn't Jon stab her?"
I said I followed the general principle of the events onscreen, but the way Dany's story ends is obviously very different. But before you dismiss me as a deranged Dany stan, I wanted to note that there still seems to be significant confusion over what exactly D&D knew about GRRM's ending. Namely, the thing that's going to be keeping people up at night the next few years is "What was the third "Holy shit" moment GRRM told them about?"
People have been trying to work Dany's madness, burning of King's Landing, or death as the third "Holy shit" moment, but…I don't think any of them work. After all, Dany's madness is supposedly "super obvious," "heavily foreshadowed," and "the obvious end to her character," so why would that be such a surprise to D&D when GRRM tells them? It's not. Nor is King's Landing getting blown up much of a surprise either; we already know there's a Chekov's Gun cache of wildfire buried under the city and it's just a matter of who sets it off. Finally, Jon killing Dany is also something that has been widely theorized for years, usually as part of an Azor Ahai/Nissa Nissa prophecy, so being told that by GRRM is not a particularly shocking thing either.
No, I think the answer is a lot simpler: the third "Holy shit" moment is Bran becoming king. D&D said the third moment happens "at the very end" of the story, and Bran being king was a generally obscure theory within the fandom, something that only really starts to make sense in hindsight like the best of GRRM's plot twists.
I did try to match the season 8 events more closely; for example, I tried to come up with a way for Jon to stab Dany as part of the Azor Ahai prophecy, but nothing really made sense. The idea that Jon just sticks his sword into Dany and it lights on fire and he starts wrecking White Walkers is too Hollywood for GRRM. This is why I fell back on the theory of Dany as Azor Ahai.
"If you're so smart, how come D&D didn't just do this instead?"
I think D&D have two fundamental misunderstandings or issues with ASOIAF. I think they have little interest in the supernatural aspects of the story like the White Walkers, and I think they value violent resolutions to character arcs instead of peaceful ones. One of GRRM's central ideas when he created this series was to deconstruct Lord of the Rings, and one specific example he provided was "What does Aragorn do with the baby orcs?" I don't think it's a coincidence that we are introduced to a baby White Walker. The White Walkers are a real culture. They're not mindless weapons of war. They are the deconstruction of Tolkien's orcs, monsters created as weapons who could have a real civilization if they were freed from the magic that created them.
I think that GRRM told D&D a bunch of complex magical and mythological stuff about the White Walkers and how they're defeated, and D&D yawned and fell asleep. The show has never been interested in any of this. So they decided, at some point, to create a more bog-standard Hollywood ending where the White Walkers are just a generic bad guy force that gets taken out by a single blow. But they also knew this wasn't a good, climactic ending to the series, so they swapped this battle with the King's Landing siege. "It's called Game of Thrones, after all, and we need to end the series with the game of thrones." But now they have a serious problem with Dany's character arc, which is deeply tied to this proposed ending with the White Walkers. Now they need to come up with a completely different explanation for why she blows up King's Landing and how she dies. So they consult their ninth grade history textbook, quickly pull an "absolute power corrupts absolutely" message out of their asses, and throw it in there.
I think that D&D were also unattracted to the idea of a peaceful resolution to the series' main conflict. The idea that the White Walker battle is resolved in a peaceful way, with the White Walkers returning north to their own civilization, is something they felt the audience would find anticlimactic. They've spent seven seasons training the audience to love bloodlust and war. The only way they can end it all is with more bloodlust and more war. So the Night King gets stabbed, King's Landing goes boom, Dany gets shanked, and then everything ends happily. This is not GRRM's way.
"Where's the Scouring of the Shire?"
I think people take GRRM's appreciation of the Scouring of the Shire too literally. The point of the Scouring is not that "a big battle happens at the end of the book," it's that "life goes on after war, and we are all forever touched by it in some way." The conflict for the Iron Throne is over, the White Walker threat has been ended, but life goes on as normal. There is a political vacuum in Westeros, one not easily filled by a ten minute scene of people voting on Bran to be king. Everything doesn't just wrap up nicely with a little bow on top. Jon is traumatized by the loss of Dany, several kingdoms are on the verge of open rebellion, and a mysterious new culture that nobody understands is now a player in Westeros. Things are not the same as they were before.
"How do these events play out in the books?"
I think Aegon is on the throne when Dany shows up, and that Cersei is a captive. The general events of the King's Landing battle will play out the same way, with Jaime, Cersei, and Aegon all dying. The books are so far behind the show and so complicated that it's hard to predict where characters like Euron end up in all this.
"Dany goes nuts, you idiot. Her Targaryen madness gene kicks in and she kills everybody and then Jon stabs her, you moron. Get over it."
Maybe. We'll see in twenty years.