She did not care if she killed innocent people as long as she got to Cersie. Tyrion had to tell her throughout that she should play it safe and find another way because Cersie will use the innocent people. HAD to be CONVINCED.
Throughout the show, she has had to be convinced not to do bad things that she would have done if not for the advice.
Now you add the fact, that she has lost everyone close to her because of that place..seeing her finally snap is not shocking at all. She tried doing what others told her, and in the end she had nothing left. She became her trueself.
If people want to complain about the writing or the short seasons, that is fair. Ultimately I think she will have the same arc in the books. I am just not understanding people who think she was some saint and then one day got up and killed innocent people. She has been a killer, she doesn't mind doing it whether it was justified or not.
This doesn't add up completely. She lost alot, no doubt about that. But Tyrion(as you pointed out) was on her council and was still there advising her. Jon(who has been a huge part of keeping her sane) is still there.
Either way, she hasn't done anything in the past, close to this level of horror of what she did to KL. She's burnt rapist and slavemasters in the past, but what she did to KL was diffirent.
But what's missing in alot of this is, we've always got alusions to the Mad Queen possibility, merely based on her father being the Mad King and thus folks being leery of Targaryen madness. Not because she's actually committed barbarous acts to this point. Even then, it took her own father years and years of hearing voices and delusions to finally go mad and snap. If you wanna argue the show had allusions of Dany being a an incompetent ruler because of her struggles and failures in Mireen than that's one thing. But there's a huge difference between being a bad ruler who makes mistakes, and becoming an unremorseful, unrepentant sadist overnight. Her arc has never had her killing the innocent. At least not in one fail swoop with no real explanation.
Dany capturing Cersei and then enacting her revenge on Cersei, and then letting her sit the Iron Throne and explore the depths of her madness via paranoia towards Sansa, The North, Jon, and where other Kingdoms loyalties lie, would've been a much better way to delve into the "Mad Queen" arc, rather than having her burn down a bunch of innocent ppl she had absolutely no interpersonal beef with. Especially considering she had no reason to do it because she already secured the victory. It would've been a better arc, because it would leave many to believe that Dany is "The Hero" and finally did what she set out to do. Rescuing KL from Mad Queen Cersei, but then subverting that trope by slowly struggling but failing not to become "The Mad Queen" and struggling but failing not to become her father.
It'd make so much sense, considering the Kingdom was already split between their hatred of the short lived Lannisters Dynasty and their hatred hatred for the past Targaryens Dynasty. Even in The North they could deeply explore the arc about the Northsmen secretly trying to push Jon towards the throne or questioning if Jon's loyalties lie down South with the KL or with The North. That arc would perfectly fit with Jon's Honor vs Duty vs Loyalty arc, since he pledged fielty to Danrys.
^^^^Even if the afformentioned was too much, something as simple showing the soldiers refusing surrender and showing the depths that dany would go to seize the throne would've been better way to do it.
Hell, showing Dany kill Cersei, take the throne, and then showing the Westerosi's rejection of Dany's "Savior Complex" slowly driving her to that Targaryen madness would've been a better storyline to end Dany's arc. There's too many ways they could have gone than to justify that episode. Too damn many.