After watching the latest episode and the scene where it appears Kate's name wasn't written on the cave walls, I'm going to go out on a limb and say that Kate was never meant to be on the island in the first place.
Flash back to when she was a child and got caught stealing the lunch box, and Jacob visited her and told her to be good from now on. This was Jacob's way of intervening in her life to prevent her from ever getting on the island. Jacob hoped that by intervening he could teach her a lesson and not to be a bad person, and this would change her life for the better, and in turn, stop her from murdering her step-father. They're obviously major differences between stealing a lunch box and murdering her step-father, but Jacob hoped that his appearance would teach her the lesson of right from wrong and to always be good, and arguably this failed, as she's now wanted for murder.
Now is the question of why would Jacob not want Kate to be on the island? I assume the simple fact is that she's been a continuous distraction for potential substitutes, to protect the island. She's arguably the reason Jack ever wanted to leave the island, or at least be so adamant about getting home, as it was in his nature to protect Kate. Kate is arguably also the reason Sawyer ever tried to get home on the raft, as he also wants to protect her.
Obviously, this theory would say that Jacob doesn't always have the power to change the future, and his "touch" doesn't always work.
There could have been a whole string of people Jacob visited to make sure they didn't get on Flight 815, as they would somehow prevent a worthy substitute their job, but we didn't see these encounters as Kate was the only one who managed to change fate, and somehow the events in her life led her to the island anyway. Maybe this was down to US Marshall, Edward Mars, who "coincidentally" caught up with Kate in Australia, forcing her on the flight after all. Leaving it out of her hands, as it would appear she was the only one on that plane who wasn't travelling at her own free will.
Of course this theory has its holes, and it could be reversed to say that because of her, Sawyer & Jack are STILL on the island (Sawyer jumped from the helicopter / Turned around the Submarine because of Kate. Jack however claimed he wanted to go back for the ones left behind, or was it really because he thought it was the only way to bring him and Kate closer together? Different theory all together!).
This theory could also be disproved by Jacob's visit to young James Ford. He also told him not to hold on to that anger and resentment, but James did, and James going to Australia to find the real Sawyer (to get revenge) is what put him on that plane in the first place, but maybe Jacob knew James couldn't change and it was inevitable that he would seek revenge. Whereas he genuinely thought he could save Kate, but he didn't.
A very open theory, but think there is something in this, especially with her name not being visible on the wall, of course if it turns out that it is next week, this whole theory is redundant.