But they do, Cersei claimed it for herself. With the High Sparrow and the Faith Militant out of the way, along with Tyrells, who's going to say otherwise? She still has all of those Lannister troops under her command, nothing but yes men on her small council, the White Cloaks and Ser Mountain, along with (presumably) the Gold Cloaks as well. With all of that, nobody in King's Landing is going to dare dispute Cersei's claim, esp. with her being the only other living blood relative of Tommen to speak of. Besides,with no heir most people probably don't have too much of a problem with her taking the crown if only to avoid a war of succession with another civil war as various houses and factions fight for thhe Iron Throne, particularly since the last one wasn't all that long ago and memories of it still fresh in some people's minds.
Speaking of Cersei and the crown,did anyone else expect her to pull a Napoleon? I was, and was a bit surprised when it didn't happen, she seems arrogant enough to do something like that, doesn't she?
Cersei taking the throne is a prime example of the tendency, especially in the early and high medieval eras, for the crown to go to the "man on the scene." At this point in time, rules of royal inheritance were a lot foggier. For that matter, so were the notions of "kingdoms" themselves. Often, it was less a question of who had the superior claim (e.g., who was closer in blood to the last ruler), and rather one of who was present to be crowned in the same fashion as the last guy.
Example:
After the death of William the Conqueror, his three surviving sons, William Rufus, Robert "Curthose," and Henry, were each given inheritances. William Rufus was made king of England and became styled William II. Robert "Curthose" became Duke of Normandy (styled as Robert II of Normandy). Henry was given money to buy land. William Rufus and Robert each agreed to become each others' heirs. Yet when Robert died (shot by an arrow in a hunting accident....or was it?!?!?!?!?!), Henry raced to Winchester (then the seat of power for the Norman nobility), grabbed the treasury, and then dashed off to London where he was crowned. Robert was away on crusade, and was basically broke (having mortgaged his duchy to William before William's death). The key factor? Henry (who became Henry I), was the "man on the scene." He was the first to get to London to be crowned, and he had the cash to back up his rule. Robert was simply in no position to contest him, even though he had the better legal claim, having been named William's heir by William himself, and anyway being older than Henry and therefore presumably next in line for the throne. Henry was there, so Henry was king.
The same thing happened when Henry died. Henry's only legitimate son had drowned before his own death, and he had only his daughter Matilda, whom he named as his heir. Meanwhile, Stephen of Blois, one of William the Conqueror's grandsons (his mother was one of William's daughters), was rich, and was in position to race to London to be crowned upon learning of Henry's death. His own elder brother Theobald was therefore passed over, in spite of arguably having a better claim, and his cousin Matilda was likewise passed over in spite of having been explicitly named Henry's heir by Henry himself. Once again: the man on the scene prevails.
Cersei has literally no legitimate claim on the throne. Even Robert's claim was based on the fact that he had Targaeryan blood through his paternal grandmother. Cersei, though? ZERO Targaeryan blood in her lineage, at least based on what we know. You'd have to go something like 4-5 generations back, by which point, it's barely worth mentioning. Her claim is based on proximity and wildfire alone.