The series originally was to focus on her, as Jack was supposed to have been killed off at the end of the pilot episode (to bump up the reality factor).
If Kate was to be the focal point, and thus dying in the bamboo field while any of her fellow survivors left the island, does that really change things?
In reality, it was Kate's gunshot that took down MIB/Flocke, not Jack's hand to hand combat. Jack merely kicked the body over the cliff. Instead of going with Kate and Sawyer, and to rescue, Jack sacrifices himself to stay on the island (presumably so he would not bog the other two down; but none of them knew the condition of the Ajira plane or whether it had already taken off). In some respects, Jack's "sacrifice" was not much since if he wanted to be with Kate, he would have asked her to stay on the island or he would have gone with her to the Hydra Island. But since he did neither, it could only mean that he was over her. He had nothing left to go back to.
Would have Kate made a similar and fatal choice?
Probably not. She was a runner. She kept on the move, one step ahead of trouble. She would have wanted off the island as badly as Sawyer. If she had injured herself in the final battle with Flocke, she would have gone great lengths to get back to the Ajira plane, not for Claire sake (again, when Sawyer and her left the island for the plane they had no idea if Claire was there or even if she was still alive). Kate's inner core was one of self-survival. Her independence and cunning kept her one step from the law most of her adult life. She would not have wanted to give up and slink off into a jungle clearing to die a lonely and undignified death.
So there would have been no emotional string pull that many fans had when Jack closed his eyes for the last time if Kate was the lead player.
