She was the character most likely to be in the middle of the action. She visited five of the Dharma stations (Swan, Staff, Hydra, Flame and Tempest). She was probably on the most "missions" or jungle treks of the survivors. She was often the one (because her "tracking skills') to get her fellow castaways from point A to point B. As a result, Kate was the most captured/tied-up character on the show. This would put her in the center of the drama and danger being shown in the series; a proxy for fan involvement with the other characters.
Kate was also the point of conflict between Jack and Sawyer; and at times, between Jack and Locke on how things should be decided amongst the group. As the fans love-hate relationship grew, that feeling was also mirrored within the scripts for Kate's character.
She also had the most consecutive centric episodes: Pilot, Part 2, Tabula Rosa, Born to Run, Exodus, Part 1, There's No Place Like Home, Parts 1,2 & 3, LA X Part 2 and What Kate Does. It would seem that the writers wanted the viewers to identify with the Kate character and her motivations. Kate's name may be derived from that of a character from John Steinbeck's Nobel Prize-winning novel East of Eden. Catherine is one of the main antagonists and, like Kate, sets her parents' home on fire as a young girl (killing both of them, as opposed to Kate who just kills her step-father) and spends most of her life from that point forward running from the law. Catherine later changes her name to Kate to further avoid detection.
Katherine is a Greek name which means "pure." Pure is defined as being not mixed or adulterated with any other substance or material; without any extraneous and unnecessary elements; free of any contamination; wholesome and untainted by immorality, esp. that of a sexual nature; and perfectly in tune and with a clear tone. Kate's character was an unyielding, stubborn, independent woman with personal flaws in morality and judgment. Her inner conflicts paralleled the island conflicts in many ways.
She was one of two characters to have actually left the island twice (the other being pilot Frank). She was the celebrity-trial centerpiece of the Oceanic 6. Her story with Aaron was the compelling reason NOT to go back to the island. She was also the reason Jack turned into a bearded, drug-addicted, suicidal mess.
When she leaves the island for the final time, she is only one of five main characters to be alive.
As for the Numbers, Kate was in 108 episodes. Kate is the only one of the Oceanic survivors and candidates whose candidate number is not one of "The Numbers" or a multiple thereof. The only survivors on the list in addition to Hurley, Locke, Sawyer, Jack, Jin and/or Sun, and Sayid are Kate, Michael, and Shannon. Shannon's number is 32, a multiple of 4 and 8 and Michael's number is 124, a multiple of 4. Kate's number is 51, which is not a multiple of any of the numbers.
However, she was the "variable" in the final equation. Even though her number was crossed off the candidates list, Jacob gave her the opportunity to take over his guardianship. As a result of still being a candidate, Kate was in the position to fell Flocke, who thought she was no longer a candidate, with a bullet.
She is also the second-to-last person to be awakened prior to Christian's funeral in the sideways world. Jack was the last to be awakened, which makes the story foundation come back full circle since it was supposed to be Kate to be the leader after Jack was to be killed off in the pilot episode.
She also served the purpose of giving Jack someone to move on with into the next stage of the after life. For Kate not to be by his side at the end would mean that Jack's island sacrifices would have no reward.
