The reason the Mad Queen stuff doesn't work is that I've yet to find a clear consensus on what Dany's motivation is. This is a significant major character and nobody is sure what truly motivated her or what she's thinking.
I've seen three schools of thought:
1. Dany has truly gone insane like the Mad King, implied by her actions and the voices she hears during the Previously On. Oh wow, the show is taking a nihilistic stand on nature vs. nurture! It's depressing, so that means it's deep!
This would justify firing on her own soldiers while skipping over the Red Keep, except that Dany doesn't think burning down a city will cause her to transcend and become a dragon or some shit. The Mad King was really, truly insane and had been for a long time before he committed his worst act. There's not a great deal of parallel to be had in their stories.
2. Dany was Mad about her dragon and friend and wanted to seek revenge on a piece of shit ruler. That's only fair, right?
Sure, except this doesn't explain why she skipped over the Red Keep and put her own army at risk. Further, D&D themselves said the burning of the city was not premeditated. So this motivation is garbage.
3. Dany felt empty and alone after her victory and said "fuck it, burn em all." If only Jon had done his part and had sex with his aunt.
I actually have the most sympathy for this motivation, but the least amount of time and effort was put into developing it. This motivation requires a ton of historical context and internality that we don't get and, frankly, it turns her character into a weak, unlikable asshole that's a mile separated from the Dany we grew to know.
The real problem is that D&D thought it was better to film the battle from the perspective of those being destroyed in order to make a comment on war, instead of putting us in the head of a major character with only 2 hours left in the series. Because of the third person limited perspective that Martin employs, this never would have happened in the books. We would have seen at least some of this story through Dany's eyes and her motivations would have been explored. Instead, we got this shit.