(Here she is just after making the "we're going to liberate THE WORLD Eternal War Lenin" speech.)
One explanation for the situation I'd heard was that the show was supposed to be ten seasons of ten episodes and the creators rushed to finish up the planned storyline in eight seasons, one of which was a lot shorter. If Danaerys had a full season or two to fall into despotism, it would be a lot more convincing.
So here are some ideas I had on obstacles Danaerys would face even if she hadn't burned King's Landing and lived to take the Iron Throne:
*During her time in Essos, she sacked the city of Astapor, a city heavily dependent on slavery, and set up a council of educated former slaves to run it in place of the obliterated master class. Said council was soon overthrown by a demagogue who misgoverned the city and it ended up getting destroyed by armies from the other Free Cities eager to re-establish slavery. She forced the city of Yunkai to free their slaves and they re-enslaved them as soon as she was far enough away. She tried to govern Meereen herself to avoid those disasters, only to face an insurgency of former slave-holders and issues with slaves who didn't know how to live as free citizens, to the point at least one former slave (a teacher for a rich family) even asked to be re-enslaved.
In her defense she does come up with a way around this (former slaves could work for their masters on a contractual basis), but my point is that she has a reformist agenda that won't sit well with the local elites. A former Targaryen queen forced the nobility to abandon the right of First Night, but she was in a much stronger position with a dragon of her own and the ear of her husband, the king of all Westeros who commanded more. Danaerys has only one surviving dragon, her most loyal troops are foreigners (Unsullied and Dothraki), and she has minimal experience as a (successful) ruler. She might get a lot more pushback on any attempts to "break the wheel" she undertakes, especially in areas where the pre-war political structure hasn't been utterly destroyed. I'm reminded of Simon de Montfort, who led the English barons against the king in the name of protecting their rights against an overbearing king, but lost the support of the barons because he defended the rights of the commoners and low nobility against overbearing barons using the same logic. He was also heavily reliant on foreigners--in this case the Welsh--which didn't help.
*The murder of Ned Stark by the Lannister regime and Robb's military victories reignited Northern separatism and even though "the Kingdom of the North and the Trident" was ultimately defeated, this separatism continues under Ned's daughter Sansa. Although a lot of the Danaerys/Sansa friction came off to me as a bunch of "I don't like my brother's girlfriend" high-school catfighting (remember in-story the surviving Starks and Danaerys herself are in their late teens or very early 20s), there're very real political concerns there even if they weren't expressed as coherently or intelligently as they could've been.
*Based on Danaerys' speech to Jon on Dragonstone she isn't religious and even seems disdainful of the idea the gods or a God (i.e. R'hllor) had any role in her success. If she doesn't tone down the hubris and at least pretend some piety, that's going to alienate the Faith of the Seven (i.e. the religion of most people). And if she does adopt a religion for political ends, it's probably going to be the Faith like her Valyrian ancestors did, not the Old Gods. Even though neither faith is exclusive of the other (oaths are sworn "by the old gods and the new"), this could be an issue with Danaerys' Northern subjects, who are already skeptical of outsiders to begin with. They could see the woman whose most successful Westerosi supporters practice one religion adopt the faith practiced by her least successful supporters (Tyrells, Martells) and outright enemies (the Lannisters, Tarlys). Politically that would be the wise thing to do, but that doesn't mean people won't be annoyed, especially if they're looking for reasons to be annoyed.
*Cersei wooed Randyll Tarly to her side by appealing to his xenophobia. If she engaged in a wider attempt to undermine Danaerys by telling everybody she's a dangerous foreigner who'd let her Dothraki warriors rape women and would turn all the men and boys into Unsullied, much of the population would be inclined to resist her rule even if she's the most well-meaning person in the world. Just because something is wrong doesn't mean people won't believe it. It's my understanding many Russians viewed Napoleon as the Antichrist, even though Napoleon's government ended a lot of feudal repression in Western Europe.
*Danaerys granted the Ironborn independence under Yara Greyjoy. Yara is later part of the council that makes Bran king so that might not have lasted very long (the Iron Islands probably lost most of their fighting-age population in Balon and Euron's various schemes), but if the Ironborn remain independent or even autonomous, well, the Ironborn have a very bad history in Westeros and more recently Balon raided the North and his brother Euron was one of Cersei's powerful allies. People might not like like a people who have a history of being Westeros's predatory mad dogs getting a longer leash, let alone getting off the leash entirely. They might speculate Danaerys gave the Ironborn independence so they could serve as a threat to keep the rest of Westeros under her control or even engage in ribald theories about Danaerys and Yara.
*Jon has a better legal claim than Danaerys and is more popular among the Westerosi, something the post-victory celebrations at Winterfell make clear. Tyrion was already planning a dynastic union between the two back when everyone assumed Jon was simply Ned Stark's only surviving (non-disabled) son and in his conversation with Varys after learning of Jon's true parentage seemed to think this would still be a good idea, but upon learning Danaerys is his aunt, Jon is unwilling to sleep with her. Even if Jon decides to take one for the team and marry her to secure the realm (given how Westeros is based to a large degree on medieval Europe and was historically ruled by a dynasty that engaged in even more incestuous practices, this probably wouldn't be unusual), this isn't going to be a happy situation for him and Danaerys--whom to her credit legitimately loves Jon--is probably not going to be happy about his being unhappy. And if Danaerys' mental stability starts to slip, she might come to view him as a threat by virtue of his not enthusiastically putting out enough.
*Gendry, the late King Robert's illegitimate son, is raised to the lordship of Storm's End by Danaerys, making him one of the highest-ranking nobles in the realm. However, he's uneducated--he might not even be literate--and might face a lot of resistance by the remaining nobility of the Stormlands even if he is Robert's son. In the books Davos feared Stannis's lords would never obey him because of his common origins and lack of education and I did come across an "after the war" fan-fic where some distant born-noble relative of King Robert rebels against Gendry. Between nobles who resent having him around, period, and nobles who only support him because they think they can manipulate him, the Stormlands might not be a pleasant place even after Danaerys wins.
So putting all these different factors together, here's how Danaerys could more believably overreach and need (or "need") to be put down in a hypothetical Season Nine (or Ten, if the war with Cersei is dragged out)...
As the new queen, Danaerys might be able to rule the Crownlands-Reach-Stormlands core in the way she'd like by installing her own people that she's better able to control simply because the local nobility have likely all been obliterated (and Gendry in the Stormlands and Davos in the Crownlands, having risen from poverty themselves, might be sincere allies in "break[ing] the wheel"). However, the North, Westerlands, and the Vale are comparatively intact and their nobility likely retain significant power. If Danaerys meddles in their local government--and especially if she uses non-Westerosi like Grey Worm, "upjumped" commoners like Gendry and Davos, or people who transgress societal norms like Brienne of Tarth to do it--that's going to spawn resentment.
Given how, at least according to Roose Bolton, the First Night is still illegally practiced by at least some Northern nobles, I could imagine Danaerys taking issue with that both due to its illegality and her own history as a victim of sexual abuse by her brother, by her rough husband (at least at first), and by the "Dothraki dudebros" who would have raped her if she hadn't set them on fire. Her investigating that could be (or is seen as by others as) as a pretext to meddle in the affairs of a region already chafing against the Iron Throne, even if a Northerner is Danaerys' consort. An offended Sansa, who already dislikes Danaerys, uses this as a pretext to declare independence and other regions, whose leadership is fearful of losing their own prerogatives, join in. Gendry will likely support Danaerys, but would face unrest at home. Between her family's own history of mental problems and with her marriage souring, Danaerys is not in a good mood and she deals with the situation overly aggressively with her army of foreigners, Southerners (possibly including emancipated serfs who bear particular grudges against nobles), and Ironborn. That aggravates the situation, especially if her supporters engage in war crimes. If Sansa is the leader of the revolt (and Danaerys in her twitchiness blames Sansa and Northern sensibilities in general for her own difficulties with Jon), Danaerys might bypass the Vale and go for the North. Drogon burns Moat Cailin and Danaerys threatens to do the same to Winterfell itself. At this point Jon has had enough and to save his sisters and childhood home, he kills Danaerys.
(Even though marital problems with Jon are a contributing factor to this whole mess, she might not see this coming--she didn't seem to see this coming in the series finale, even though she knows he's rejected her romantically and that he's objected to her torching King's Landing and ordering her soldiers to kill prisoners.)
This would also set the stage for the elective monarchy at the end--the Targaryen dynasty fails due to madness, the Baratheon dynasty fails due to incompetence, and then the restored Targaryen dynasty fails due to madness (or what is perceived as madness--a totally sane but less competent monarch could still end up in this pickle). If Jon is killed in the process of taking out Danaerys or soon after (Drogon should've done it rather than torch the Iron Throne), the nobles might choose a new dynasty completely--and if they're afraid that a too-absolutist government might threaten their privileges, they might deliberately pick a weak new ruler. In that case you could still have King Bran, or if his magical abilities are viewed as too weird or threatening, a well-meaning non-entity like Edmure Tully. Tyrion, assuming he doesn't get killed earlier (Danaerys killing him could prove--or depending on what he does "prove"--that she's gone too far) could be the architect of this plan, just like in the show.
So what do you all think? I'm not planning on writing a fan-fic, although I've sent some of my ideas to the author of the Danaerys-rules story "Break The Wheel."