As a nation so firmly tied to records, it would have been inconceivable that they would not have written about this experience. In spite of that fact, the Savior commands them to write. Since he was commanding them to do what they would naturally have done, the question is why Jesus made that request.
The purpose is intertwined with the first Nephi’s vision of a book coming from them to the world. It was intertwined with Mormon’s record. They were to write so that it would be in the Book of Mormon, and so that when the Book of Mormon came to the word, the Gentiles and the remnant of their seed would have these words.
The purpose was part of the beginning of the end of the scattering of Israel. It was an important beginning of the process of gathering “them in from the four quarters of the earth.”