While I personally do think that "Mad Queen" will be in the books in some way, shape, or form (as the whole point of the dragons thematically is that winning using such a destructive force renders victory pyrrhic), everyone pointing to that as a reason for last night's laughable absurdity is ignoring the fact that it still made no sense whatsoever.
Even if we are to draw parallels to Aerys II, it's important to note that he grew steadily paranoid and crazy over many years. His ultimate insanity was a gradual process that was the result of multiple events. Further, his defining act as the Mad King - attempting to burn down King's Landing - was a premeditated scheme meant to deprive Robert Baratheon of the capital if it looked as though he was going to win. His "burn them all" moment wasn't some final psychotic snap - it was him realizing that the rebellion was about to be won, and an order to Lord Rossart to ignite the wildfire caches he had hidden away for that exact purpose many months before, directly following Jon Connington's loss at Stoney Sept.
So, no, Daenerys final breaking point does not make sense even in comparison to the Mad King. With Aerys, we know why he acted the way he did. Here? Well, D&D said that Jon rejecting her was the "trigger," or however they put it. She even agreed to Tyrion's surrender conditions before the battle, and although she has felt great loss this season, has been speaking out against tyrants every chance she gets. And then, after certain victory, decides to massacre innocents needlessly? They made little to no effort to explain why she opted to simply slaughter civilians in the street after complete victory was secured. They just did it for the shock and awe twist. That's all the show has been about for years now.
As a young girl, her family is butchered and she is shipped halfway across the world into hiding.
She grows up with nothing but stories of the throne she was promised, and an abusive, entitled older brother who claims he deserves it more. When that brother dies, she sees an opportunity for the throne to be hers specifically, and to justify all of the suffering she has unfairly endured.
When she gives up for the first time (after losing her husband, and his army) she walks into a funeral pyre and yet emerges with three dragons – a miracle, if ever there was one, and surely a sign that she is meant for great things.
She does her best to lead her people through feast and famine, all in the name of one day claiming what is rightfully hers. She has a string of very mixed results while trying to rule, but we tell ourselves that these are the failures of a great future leader and eventually it will all have been worth it.
Then she does the unthinkable and crosses the narrow sea with three dragons, a Dothraki horde, and an army of fiercely loyal fighters, where a handsome king in the North who is loved by most asks for her help in saving the world. Of course she does the right thing and agrees to help him.
But in doing so she is punished – first by fate, in losing one of her dragons, one of her most loyal subjects, and half of her army, and then later by the Queen who promised to join her in saving the Kingdom. That same Queen repays the favor by killing one of her dragons and beheading one of her few friends. The Queen's subjects - who she was promised were still loyal to her family after all this time - remain indifferent.
Oh and that King she fell in love with? Turns out he has a better claim than she does, everyone loves him more than her even though he doesn't want the throne or her hand in marriage, and even her own closest advisors betray her by spreading word of who they want on the throne. Not her.
And so a woman who has grown up envisioning this day her entire life, finds herself humiliated and alone with exactly one advantage left to press: a dragon. And when her enemies – the same enemies who have picked at her every ounce of mercy she has ever shown, who would have gladly seen her shot out of the sky and dragged through the streets – decide that they would like to conveniently surrender, she looks at the Red Keep and remembers what happened to her father, her family, and her friends, and all that they suffered.
Thus she snaps, and decides to rule through the only advantage she has left: the fear of her dragon, of fire and blood and absolute power, and the stories that will be passed on after this day.
The civilians of this city mean nothing to her at this point, even if they might have had things played out differently. Others created the context of her madness, but she makes the choice.
She is a tragic hero.