- She reacts to a defeat in war by inflicting a defeat at the Lannister forces, offers a choice to Tarly sr. and son, and when they refuse, she execute them. Yes, harsh and unnecessary. Bad mistake on her part. But not done out of cruelty.
I'm of the position that Daenerys has always (or at least since her arrival in Meereen) had instances that suggest a "mad queen" potential (here referring to tyrannical, merciless and being too quick or fond of burning people, rather than literally being insane - the "mad" epiphet is mainly just because of parallels to her father's fondness for burning people). Throughout the seasons I was a little confused about where the show was going to go with it, because it didn't seem like it would work if it wasn't building to something like this. It's normally clear in a TV show whether the audience is
intended to agree with or sympathise with an act, even if you could think about it and disagree with it independently, normally you can tell whether the portrayal was meant to be sympathetic or not. And it really seemed to me that the show was building in these instances of Daenerys doing things that were clearly problematic or at least showed potential of building up to being problematic down the road (and here I'm not talking about the morality of events in universe, but how they are portrayed to the viewer). And there was usually some sort of conversation afterwards that reflected on it a bit, but to me it always felt quite inconclusive whether we were supposed to see it as maybe a mistake that she had learned from or not - so I was confused about whether the show intended that those incidents were firmly behind her (as they didn't feel like it, but it could obviously have been a poor portrayal of that), or if they were indicative of something that could cause future conflicts.
The execution of the Tarlys was by far the most prominent example, I think your quick description has minimized the impact and significance of what happened and particularly how.
We're dealing with a fictional world here so obviously their standards and morals are not the same, but within the world of Westeros, executing someone by burning them alive is considered more heinous than other forms of execution. We saw Jon Snow execute someone by shooting specifically to spare him the suffering of being burned alive. The other burnings conducted by Melisandre and Stannis were similarly treated as more problematic than simple executions. So burning prisoners alive will be looked on differently than "cleaner" executions. And I'm not making the argument about the technical level of suffering caused by each of these executions in reality, only how these acts seem to be percieved in Westeros.
Also, while burning people alive doesn't seem to be looked on too fondly in general, in Daenerys' case it specifically links back to Aerys. Burning a high lord alive was what started the rebellion. And Aerys increase the frequency of his burnings as he got worse (culminating of course in "burn them all!", though that part is not widely known in Westeros). So her specifically returning to Westeros and then immediately burning people alive will set off alarms for many - and that's regardless of how justified the executions are. That's something she should have known, and the fact that she decided to burn a Lord and his heir despite the fact that she had every way of knowing the obvious problems that would pose should cause concerns. Because either she was somehow oblivious to it, or she was so keen to burn people that she proceeded with it despite the obvious problems.
So why did she want to burn them? I've seen comparison made to killing enemies that refuse to surrender, but it's important to note that wasn't the case here. Randyll and Dickon weren't still fighting so they had already surrendered. The choice that she offered them was to "bend the knee and join her" or die, which is not simply a matter of surrendering. Tarly obviously refused, but he was still her prisoner. There was no particular need to rush the decision of what to do with him - he could have easily have been taken and put in a dungeon or under guard somewhere. She didn't do it because "if putting people in chains becomes an option, many will take it." That statement is strong evidence of her all or nothing approach when it comes to loyalty, the "kneel or burn" attitude that I think is ultimately what will cause problems rather than outright cruelty. Her approach is to make an example of her most prominent prisoner by burning him and his heir alive to demonstrate to others that they face exactly the same choice - burn or kneel.
And there's the matter that it wasn't just Randyll, but Dickon too. Randyll disrespected her by making clear he was going to refuse to acknowledge her as queen. Dickon was simply someone who was present when his father was about to be burned and wanted to stand beside him. Daenerys justified her action with "I gave them a choice. They made it." But the "choice" put to Dickon was hardly a fair one and, importantly, she wasn't forced to present him with that choice or abide by what he said. As their captor it was easily within her power to simply restrain Dickon or have him taken away regardless of his protests. Or she could have taken them both as prisoner (remember, there was no rush to deal with them). Perhaps given an hour or two Randyll might be able to convince his son to bend the knee. Or perhaps Tyrion could convince Randyll to reconsider his "take the black" option as an honourable way out. So the fact that "it was their choice" holds little weight when Daenerys held all the power and could have done things differently - about as much weight as Aerys letting Rickard Stark have a trial by combat, then choosing "fire" as his champion.
That's a lot about a single instance, but I think what happened with the Tarlys was very significant and indicative of the potential problem. I agree that the extent that other characters suddenly increased their concerns about Daenerys in the last episode felt very rushed, but the concerns were there. And the early part of season 8 made clear that Jon's claim was going to be a problem for her, even if he didn't want the throne. That's why I said after episode 3 that I suspected the real reason Cersei still remained with 3 episodes to go wasn't because a battle to dethrone her was so significant, but so that there was a remaining obvious conflict after the Long Night rather than everything being all wrapped up, and the conflict between characters that fought together against the Others would come into the fore during that. I don't know if it will escalate to war, but the direction things are heading makes sense.