Abarbanel discusses why all nevuos, including those of Yeshayahu, Yirmiyahu, etc., are not written in their historical context in Melachim or elsewhere. For that matter, why a separate book for Tehillim and Mishlei? Why not just include them with the stories of David and Shlomo?
I will not post his entire discussion here, but the gist of it is twofold:
- It would make things difficult for readers, having, for example, Megillas Koheles in the middle of stories of Shlomo's life.
- We include in the historical books (Neviim Rishonim) only what is relevant to the life and times of the subject of the book. Whatever nevuos were not relevant to the stories of the kings we are involved with in Melachim were not included within.
Now, why do Yeshayahu and Yirmiyahu have their own books with collections of their nevuos, but Eliyahu and Elisha do not? Does this mean that Eliyahu and Elisha, and for that matter, Gad HaChozeh, Nassan HaNavi and others, did not prophesy besides what is written in Melachim? Perhaps. But Abarbanel offers another clue:
וכלל אחד אתן בידך יהיה לך מפתח גדול בהבנת הנבואות האלה והוא שרוב הנביאים האלה נבאו על הגאולה העתידה לפי שמפני רחוקה וארך הגלות יהיו בני אדם מתיאשים ממנה ולכך הוצרך יתברך להעמיד נביאים רבים מיעדים ומבטיחים עליה
That is, specific neviim were chosen to have their prophesies compiled and included in Tanach because they are relevant to the galus that we are currently enduring. Other neviim may have had scores of prophesies as well, but they were not as important for the survival of the nation.
Lastly, why are there narratives included in Yeshayahu and Yirmiyahu that are related almost exactly the same in Melachim? I would say that each sefer was written with a different purpose. Melachim was written to tell of the events relating to the kings of Israel. Yeshayahu was written to deliver the nevuos of Yeshayahu. If a story is told in both, it is relevant both to the stories of the kings and to the life and prophesies of Yeshayahu.