Kit death was avoidable

[El Juanico Diez]

Kit certainly had a natural birth. According to the writings of Beatrice and Bertrand, the danger for the babies were as they were in the womb. So if soon after Beatrice Jr began to get out of the uterus Kit had eaten the healing, kit was to survive, taking into account that the heal was extremely fast as seen in case of Olaf. After all, if she was still living enough to make strength in Beatrice Jr leave from her inside, she is likely she could also ingest an apple as it. Sunny could be beside her mouth with a piece of the apple as Klaus and Violet ended the work on the other side.

I mean, for children who have always got a way at all, I think they managed to think of something like that.

[Dante]

I agree that this is something of a contrivance, but I think we must presume that Kit's body had suffered too much damage already from a combination of shipwreck and starvation, the Medusoid Mycelium and giving birth for her to survive even with an immediate dose. The healing may well be rapid, but I don't know if we can presume it to be a magic bullet; Sunny had to rest for some time after her initial infection was diluted in TGG, and in all other circumstances it's reasonable to presume that the victims were pushing themselves to the limit to act. The Baudelaires were young and healthy and, in the desperate circumstances of The End, were able to rush down to the coastal shelf with a full stockpot of apples; but Olaf and Kit, through one mortal injury or another, could hang on long enough only to perform one last deed for the future.