Well, if someone blows up the Vatican and kills the heads of most major houses, he or she will not be crowned as the regent. He or she will get killed for this. Of course, people don't have proof of Cercei's crimes, but they would suspect her. Heck, they would probably even suspect her of killing her own son/ the king, that's like two huge crimes rolled into one. In the show, the Lannisters are a spent force, their gold mines are exhausted and the crown is in debt. Their army is stretched thin after years of war. Nobody would support her claim for the throne.
Show Cercei is queen, not because it makes sense, but because the show makers like the narrative.
In the North, nobody should support the bastard Night's Watch deserter son of Nedd Stark, who had his army slaughtered, because he himself broke with the battle strategy and had to have his ass saved by Littlefinger. And why does nobody care, that he was resurrected from the dead? Show Jon is king, not because it makes sense, but because the show makers like the narrative.
Book Dany is obnoxious as well, but at least there are hints, that she might turn mad (which makes her a bit more interesting). Show Dany is insufferable. Should she die in the end, it would reconcile me a little bit with the show.
And the Arya plotline can't be taken seriously. Unfortunately, she is one of my favourite characters in the book
It's a dolphin!