Yes, Daenerys went full metal Targaryen on King’s Landing. Yes, she slaughtered hundreds — probably thousands, maybe even tens of thousands — of innocent men, women, and children. Yes, it was terrible thing for her to do.
But no, I don’t think laying waste to King’s Landing necessarily means she’s gone mad. In fact, I think there’s an excellent chance Dany torched that city because she knows she should have done it earlier.
She wanted to. She suggested it shortly after she and her army landed at Dragonstone. Tyrion, however, talked her out of it, saying she’d be slaughtering innocents. He was right that a LOT of King’s Landings folks would die. But I think it was a mistake strategically. Don’t get me wrong; I’m not an advocate for killing civilians — even on television or in the movies.
But look at this from Dany’s perspective. Look at what’s happened to her as a result of NOT attacking King’s Landing. First, she gets sidetracked by fighting against the White Walkers. It was an admirable decision, but she’d already lost a dragon to those fuckers. The battle at Winterfell also cost her most of her Dothraki, and at least half of her Unsullied. Not to mention Jorah.
To make matters worse, when she started south to prep for dealing with Cersei, she learned that the Wildlings were staying behind. Okay, they weren’t a disciplined army, but they were enthusiastic, and that counts for a lot. And THEN? Then just as she’s getting home, she gets dough-popped by Euron. That cost her yet another dragon, a few more boatloads of troops, her supporters from Dorne, and her last real friend, Missandei.
After that, she 1) discovers Varys is plotting against her, 2) her boyfriend has a better claim to the Iron Throne, and 3) he refuses to keep his real name secret. Basically, she’s far worse off than she was just a few episodes earlier. Even the Breaker of Chains would find that discouraging.
And Tyrion is still advising her NOT to alienate the people (who, let’s face it, haven’t shown her a bit of love even though she risked everything to keep them from being turned into fucking zombies) by slaughtering everybody in King’s Landing.
On a more positive side, if Dany had leveled King’s Landing like she wanted to, she’d probably still have at least a pair of dragons, most of her Dothraki and Unsullied, as well as Jorah and Missandei.
And hey, it didn’t take long for her to destroy the city. Maybe four, five hours. If she’d torched the place when she wanted to, Dany would still have had plenty of time to tell the rest of the Lannister army to take the knee then march them north to fight Winter zombies. Plus, she could probably have persuaded House Tyrell to cough up some troops, and she already had an agreement with Dorne.
In other words, if she’d done what she wanted to do, she’d have two dragons, a bigger army, more trustworthy advisors, AND she wouldn’t have to fret about Cersei stabbing her in the back. Laying waste to King’s Landing would have been a horrible thing to do, but a smart strategic move.
So I rather think that instead of ‘going mad’, Daenerys may have simply thought, “If I do this now, folks will probably be a lot more amenable to a change in management.” The citizens of other cities, when it was time to formally bend the knee, would be saying to themselves, “Jesus suffering fuck, did you SEE what she did to King’s Landing in, like, half an hour? Bend the knee? I’ll lay flat and kiss the hem of her goddamn skirt.”
Again, this is not a blanket approval of using dragons against civilians. Just an acknowledgement that you can’t win the game of thrones without breaking a few eggs.