Nephi was not a fan of a monarchial form of government. He made this clear when he was made the king by his people in 2 Nephi 5:18, I, Nephi was desirous that they should have no king; nevertheless, I did for them according to that which was in my power. Later on in the Book of Mormon, we learn of the great destructions which came upon the Jaredites because of the wickedness of their kings. Alma refused to be the king saying, it is not expedient that we should have a king…Nevertheless, if it were possible that ye could always have just men to be your kings it would be well for you to have a king (Mosiah 23:7-8). Nephi must have had reason to trust the man he anointed to be king. Otherwise, Surely this thing leadeth into captivity (Ether 6:23).
Interestingly, Nephi does not anoint one of his sons as king. This may have been because he had no sons at all. The fact that he entrusted Jacob, his brother, with the records supports this hypothesis. There is no record in the Book of Mormon that Nephi had any sons. He makes reference to his “family” and “children” in other scriptures (1 Nephi 17:1, 2 Nephi 4:15; 5:6; 25:26) so that we know that he did have children. The context of events described above suggests that the children he had were all daughters and not sons.