About some of your doubts concerning the HBO show’s finale: given the results of Cersei’s last play (i.e. everyone else is dead), isn’t there enough of a political vacuum for Cersei to realistically be able to seize the throne without facing too much official protest about it? There is basically no credible claimant yet. The entire Baratheon/Lannister/Tyrell succession is extinct. Wouldn’t Cersei be the closest KL has to some semblance of political continuity? It is suicidal, yes, but right now?

As for a vacuum, in the city itself, there’s no one left to oppose her on the Small Council, the Sparrows are leaderless, and Cersei does have some guardsmen. But without any shred of popular legitimacy, all it takes is one good riot to bring it all tumbling down. 

And for outside the city, the Florents are the closest in proximity, followed by the Estermonts, followeed by the Targaryens themselves. Lannisters are way too remote. 

But as to continuity…the attraction of continuity is stability, security, and predictability. Cersei offers none of those things; she’s basically Aerys the Third. If allying with the Lannisters through a dynastic marriage, the closest form of alliance there is in Westeros, brings you death by wildfire, there’s literally no upside to being on her side, and no downside to opposing her because she’s going to kill you anyway. 

Dany’s arrival makes all this moot anyway. She’s got the two biggest Targaryen loyalists on her side, in the show anyway she’s got an ironclad claim to both the Targaryen succession and the Baratheon succession, she’s got an enormous army, and she’s got dragons.