Because Tolkien would have earned my undying spite if he had killed off Frodo...
Seriously, though, one thing that I have discovered as a writer is that there tends to be a "right" time and a "wrong" time to kill characters. You generally do not kill of characters when they have more to do and further to grow. It would have been easy to kill Frodo off, but it would not be right. If anything, I would kill him off at Mt. Doom, which might be more logically than the Eagles coming in from nowhere and rescuing him, but Frodo's journey was not complete, per se.
For example, with Boromir's death, it effectually "completes" his story. He did not have to die; Tolkien could have let him live and gone on with different plot wrinkles. But he had reached the point where he wanted to go with Boromir, so killing him worked. Likewise, there really wasn't anywhere more for Theoden to go when he died. He had been rid of Saruman, had led his people to battle, and was basically at peace. Tolkien could have had him go home to keep ruling, but his story was essentially finished. The third example I can think of is Denethor - his death was the logical and best way for his story to end. For him, it doesn't get better, it just gets worse, and his death is a culmination.
But not so with Frodo. Frodo is still growing and changing to the very end of the book; killing him off at Shelob's Lair or Mt. Doom is not the logical or right place for him to end.
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