Here's an interesting subreddit,
All of the foreshadowing that lead up to last night's episode
(bolding mine):
• 106 - Viserys, after seeing how much the Dothraki love Daenerys, becomes jealous and tries to run away saying “Who can rule without wealth or fear of love.” (Daenerys well echo this sentiment in 804 and 805)
• 204 – Daenerys “When my dragons are grown… we will lay waste to armies and burn cities to the ground.”
• 206 – Daenerys “I will take what is mine with fire and blood.”
• 207 - Cersei Lannister “Half the Targaryens went mad, didn't they? What's the saying? "Every time a Targaryen is born, the gods flip a coin."
• 210 – Daenerys has a vision of a destroyed throne room. She reaches out to the throne but never touches it.
• 303 – Daenerys when speaking about her brother Rhaegar “…he was not the last dragon.”
• 404 - Daenerys executes 163 Meereenese noblemen. In 406 we learn some of these men were innocent. Daenerys shows absolutely no regret.
• 405 – Daenerys speaking with Jorah. “You counseled me against rashness once in Qarth. I didn’t listen. It all worked out well.”
• 407 – Jorah tells Daenerys “The masters treated men like beasts, as you said. Herding the masters into pens and slaughtering them by the thousands is also treating men like beasts.” Reminding her “I wouldn't be here to help you if Ned Stark had done to me what you want to do to the masters of Yunkai.”
• 407 – Daenerys “They can live in my new world or they can die in their old one.”
•
505 – Daenerys executes an innocent Meereenese nobleman for the sole purpose of intimidating the other nobles.
• 505 – Daenerys reopens the fighting pits allowing for innocent men to kill one another for entertainment.
• 508 – Daenerys “I’m not going to stop the wheel. I’m going to break the wheel.”
• 604 – Daenerys murders the leaders of the Dothraki for the sole purpose of consolidating power.
• 606 – Dario to Daenerys “You weren’t made to sit on a chair in a palace. You’re a conquer, Daenerys Stormborn.”
• 606 – Daenerys to the Dothraki “Will you kill my enemies in their iron suits and tear down their stone houses?”
•
609 – Speaking about the masters Daenerys swears to “Kill every one of their soldiers and return their cities to the dirt.” Tyrion responds “You once told me you knew what your father was. Did you know his plans for King’s Landing?” Daenerys “This is entirely different!” Tyrion “You’re talking about destroying cities. It’s not entirely different.”
• 702 – Yara Greyjoy, Olenna Tyrell, and Ellaria Sand all try to convince Daenerys to use her dragons on King’s Landing. Tyrion convinces her to do otherwise. (This is important as Tyrion’s plans fail, and his repeated failures show Daenerys there’s no other option)
• 702 - Olenna Tyrell “Commoners and nobles are all children really. They won’t obey you unless they fear you.” And later. “You’re a dragon. Be a dragon.”
• 704 – After news of her army’s defeat at Casterly Rock, Daenerys questions Tyrion’s plans and his loyalty.
• 704 – Daenerys “Enough with the clever plans. I have 3 large dragons. I’m going to fly them to the red keep.”
•
705 – Daenerys executes Randal and Dickon Tarly when imprisonment was a perfectly viable option.
• 705 – Tyrion “Daenerys is not her father.” Varys “And she never will be with the right counsel. You need to find a way to make her listen.”
• 705 – Tyrion devises a convoluted plan to capture a wight to convince Cersi to help fight the night King. Over the rest of seasons 7 and 8 this plan goes horribly wrong and results in the death of a dragon. The failure of this plan further degrades Daenerys’ trust of Tyrion.
• 801 – Lyanna Mormon publically confronts Jon Snow about giving up his crown and swearing allegiance to Daenerys. This is the beginning of Daenerys’ realization that she has no love in Westeros.
• 802 – Daenerys is angry that Tyrion’s advice about Cersei turned out to be wrong. Saying “Either you are a traitor or a fool.” And “Cersei still sits on the throne. If you can’t help me take it back I will find another Hand who can.”
• 803 – Jorah is killed in battle. He has proven to be one of the few advisors Daenerys had that tried to temper her impulses.
• 804 – Daenerys sees people praising Jon Snow and becomes jealous.
• 804 – Tormund “What kind of person climbs on a ****ing dragon? A madman, or a king!” (I’d like to point out when Tormund says “madman” it cuts to a shot of Dany, and when he says “or a king!” it cuts to Jon)
• 804 – Speaking about Jorah to Jon, Daenerys “He loved me and I couldn’t love him back. Not the way he wanted. Not the way I love you.” (Her love for Jon is not returned in 805)
• 804 – Daenerys “I saw them gathered around you. I saw the way they looked at you. I know that look. So many people have looked at me that way but never here.”
• 804 – Varys “These are the people you came here to protect. Do not destroy the city you came to save…” Daenerys “I’m here to save the world fromy tyrants… and I will serve it, no matter the cost.”
• 804 - Daenerys “Speaking to Cersei will not prevent a slaughter. But perhaps its good the people see Daenerys Stormborn made every effort to avoid bloodshed and Cersei Lannister refused. They should know whom to blame when the sky falls down on them.” (We should note she is directly talking about “The People” here)
• 804 – Missandei’s final words before her execution. “Dracarys”.
• 805 – Varys “They say every time a Targaryen is born, the Gods toss a coin and the world holds its breath.”
• 805 – Daenerys speaking to Jon “Far more people in Westeros love you than love me. I don’t have love here. I only have fear.”
• 805 – After a half hearted kiss with Jon, Daenerys says “Alright then. Let it be fear.” (Echoing what Viserys said in 106)
• 805 – Tyrion “The people who live there, they’re not your enemies. They’re innocents.” Daenerys “Your sister knows how to use their enemies weaknesses against them. That’s what she thinks our mercy is. Our mercy is our strength. Our mercy toward future generations who will not be held hostage by a tyrant.” (She’s all but saying she’s not going to show mercy and will butcher everyone in the city)
• 805 – Daenerys to Tyrion. “Next time your fail me will be the last time you fail me.”
And that’s just what I can remember off the top of my head.
Here’s the point. Daenerys threatened multiple times to burn cities to the ground, she executed/murdered innocent people numerous times to consolidate power, she realized without love all she has left to rule with was fear, and she grew to distrust the only advisor trying to prevent her from burning down King’s landing.
She wasn’t “acting out of character” at any point in 805. She literally did the thing she’s threatened to do for multiple seasons.
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Video compilation of all of Daenerys & dragon "kills" seasons 1-7:
The execution of the Tarlys, and of the Mereenese nobleman by feeding him to her dragons under the pyramid were unnecessary, and excessively cruel. The latter especially since Varys later discovered that the Sons of the Harpy were funded by slavers from Yunkai, Astapor, and Volantis, not those noblemen.
There has always been a duality to Daenerys' character -- a kind compassionate side ("Myhsa"), and a very ruthless side to her --more in line with her Targaryen heritage. While she was certainly a better person than her brother Viserys, she was still essentially raised by him, grew up in his shadow and that had to have some impact on character.
All she needed was the right number of things occurring in rapid succession to succumb to her darker side more fully, which was always there. So was the inbred, Targaryen propensity to madness --just waiting to manifest under the right conditions. The writers really rushed the catalysts, but they are there: rejections, betrayals, losses.
Consider also that there have been cases of people who seemed "normal" but went "postal" -on a murder spree, their inability to handle negative events having built up in a pressure cooker. People who thought they "knew" them were mystified by their sudden rampage.
There was no getting around this, the destruction of King's Landing was a
'fixed fate', foreseen through
Dany's vision of the "snowy" ("ashy"?) Great Hall in ruins in the House of the Undying in Season 2.
Bran also saw the same ruined Hall in Season 4 along with the shadow of the dragon over King's Landing. And, even more significantly, Bran saw the dragon shadow
again in Season Six, this time juxtaposed with the Mad King, pyromancers, and wildfire explosions.
Most believed the wildfire component of those visions came to fruition with the Sept explosion, but Dany detonated her father's other old caches of wildfire that were hidden around the city.
"You've heard of wildfire? The Mad King was obsessed with it. He loved to watch people burn, the way their skin blackened and blistered and melted off their bones. He burned lords he didn't like. He burned Hands who disobeyed him. He burned anyone who was against him. Before long, half the country was against him. Aerys saw traitors everywhere. So he had his pyromancers place caches of wildfire all over the city. Beneath the Sept of Baelor and the slums of Flea Bottom. Under houses, stables, taverns. Even beneath the Red Keep itself."
―Ser Jaime Lannister Se3Ep5 "Kissed by Fire"
That angle at least makes a little more sense to me on first thought. I don’t think there’s much point to outright madness. It’s like a balrog coming in and laying waste to the city out of the blue. 
