harrenhal, king's landing, and volantis are all metaphors for the same thing, that the structural injustices which led to the creation and maintenance of these places will eventually result in their collapse. harrenhal is a symbol of the worst of feudalism, i say 'worst' because the books do romanticise certain aspects of it, oathkeeping as fidelity is clearly intended to be beautiful and moving in brienne's storyline and "the north remembers" but what harren the black did was exploit the riverlands and the iron islands and employ slaves in its construction, thousands dead for one man's monument to power and dominion over others. it was a castle built on fear, not fealty. in a non magical sense, the curse of harrenhal is hubris. it was intended to be the height of feudual power because it was virtually impregnable - impervious to 'normal' medieval warfare, but ended up being destroyed by yet another king, this time in possession of a more fantastical means of power - dragonfire (the hubris theme is strong in the main series, the castle is awarded to scheming, ambitious, and amoral political players who either engineer their own downfall or are eventually pushed off the board by someone who can scheme better them).
but the thing that interests me is that the burning of harrenhal also positions the targaryens as capable of status quo upsetting, radical change. they can disrupt existing power structures because what are walls in front of a dragon? dragons fly. the visionary bit here is the unification of the realm, which is definitely framed as an admirable thing by the narrative because of the upcoming threat of the long night—what aegon invades westeros for. i don't think the targaryens are, like, evil for being conqueror kings, that's a disingenuous reading, but i do think this is a somewhat corrupt idea of 'unification' as it is primarily focused on the dynastic interests of this one family. because the other thing he did was make the iron throne, something that's currently the biggest obstacle to the possibility of the realm uniting in the face of a common enemy. it's significant that a fight over the throne is what kills their dragons, that's a very blunt way of saying that the the iron throne is what ultimately smothers their ability to enact any wider social change, by the end they weren't any different from the other houses. so king's landing is no longer a symbol of targaryen rule, both their dragons and their dynasty died there and any vision of radical change that they began the conquest with was consumed by the iron throne. kl as a whole is symbolic of the game of thrones, the city's geography is modeled after the iron throne with the king within the red keep on top of aegon's hill and the smallfolk left to rot at the bottom. and the inheritors of 'the game' are the lannisters, the ones who swindled the city and the throne from the targaryens. tywin continues aerys's legacy of violence, aerys would burn a city out of 'madness', tywin would do it out of pragmatism ("Lord Tywin would not have bothered with a search. He would have burned that town and every living creature in it"), so it makes sense for tywin's philosophy, that of exploitative and dehumanising violence in the pursuit of power, to be the cause of its destruction. several posts have been made about why joncon and cersei are the ones haunted by the memory of tywin's crimes with reasons to want to emulate him, so i'm not going there, but i feel it's also really important for king's landing to go out because of purposeful grasping over the iron throne and without any dragonfire (even accidental) involved. king's landing is doomed in a very apocalyptic sense because 'the game' is unsustainable. nothing new will come out of the city's destruction and dany's use of fire is always transformative, she creates life out of death. wildfire only destroys.
the city dany will bring fire and blood to is volantis, not king's landing. volantis is the final remnant of the freehold's imperial legacy. a society built on systemic evil, on the backs of slaves cannot go on. the cyclical story here is obviously that of the dragons being redefined and redeemed as symbols of liberation after they historically helped the freehold perpetuate the evil of imperial expansion and slavery. i think the error lies in assuming dany has a personal connection to king's landing but she really doesn't. it used to be their seat and then the targaryens doomed themselves in westeros because of the iron throne. dany is not here to repeat those same mistakes. where she must go instead, is harrenhal. aegon burned it on the first day of his conquest, a conquest he began because of the prophecy of the prince that was promised. the castle is left in a half ruined state so it's not allowed to, like, die. the targaryens kept returning there and got involved in events that altered course of their rule forever - the council of 101 which led to the dying of the dragons and the tourney at harrenhal that led to their line almost ending. i think the narrative 'curse' at its heart is that the castle is the site of unfinished business. it was a result of excessive feudal violence and the conquest was supposed to lead to a different, better model of governance, i do think the targaryens came close to achieving that at certain points in their history because it was a reign of both splendour and horror, but in the end they also ended up being responsible for the perpetuation of that very feudal violence in king's landing. as the last targaryen, dany's destiny lies in unifying and protecting the realm during the long night, this is what they survived the doom for. and i think to do that she has to go to this castle that's a place of both narrative beginnings and endings but also in stasis, and finish what her ancestors began—what aegon and rhaegar wished to achieve at harrenhal but couldn't, one too motivated by conquest and the other by prophecy. because only then will the curse break and the song end.