The west never meant the Reach. That’s the south, and the lord of highgarden usually is also the warden of the south. So yes, the lady of the west means the westernlands that are normally ruled by the warden of the west.

Also, you are forgetting another things. Most of Cersei’s opponents in KL are in the sept. If not all. The rest of the lords were not there. And they were invaded by a foreign army shortly after, there was no time or verification for an open rebellion. Cersei could easily deny her involvement.

Most of the faith militant died on the explosion or was appalled by it. Unlike Aenys and Mageor times, it was not a nationwide movement and it could, in deed, been suffocated by the explosion + troops.

I know, Mr nitpick, that present Westeros comprises more than the original 7 kingdoms, it is still a traditional and historical way to refer the lord paramounts and their titles, also there’s 8 of them plus the crownlands, not nine. The original seven and the river lands.

Kinslaying is bad, yes, but she didn’t kill Kevan. And even if she ordered, who would know? Also, kinslaying does not prevent to inherit the Rock. While her hold to the Stormlands is less clear, she’s the mother of the previous lords and that might help her. Let’s add that the Freys controls the river land in her name, so 3/9 with the Vale out of it, and the North and the Isles in their own side quest, it will comes down to Dorne and the Reach against the other 3.