In order to discover why the Lord would place such emphasis on the latter day Gentiles in His discourses to the Nephite people recorded in 3Nephi, we need to consider the role of the Gentiles in the Lord's plan for His children. Just what is it the Gentiles are to accomplish in that plan?
The Lord has designated the latter day Gentiles as the initial couriers and caretakers of the gospel of Jesus Christ for the opening of the latter days. It was to be from the latter day Gentiles, the Book of Mormon containing "much of my gospel which shall be plain and precious" (1Nephi 13: 34) was to come forth. The Lord specifically instructed the Nephite prophets, "ye shall write these sayings after I am gone,...that these sayings which ye shall write shall be kept and shall be manifested unto the Gentiles, that through the fullness of the Gentiles, the remnant of their (the Jews specifically in this context, but all scattered Israel is included) seed, who shall be scattered forth upon the face of the earth because of their unbelief, may be brought in, or may be brought to a knowledge of me, their Redeemer. (3Nephi 16: 4)
Speaking to Nephi the Lord said,
"For, behold, saith the Lamb: I will manifest myself unto thy seed, that they shall write many things which I shall minister unto them, which shall be plain and precious; and after thy seed shall be destroyed, and dwindle in unbelief, and also the seed of thy brethren, behold, these things shall be hid up, to come forth unto the Gentiles, by the gift and power of the Lamb. And in them shall be written my gospel, saith the Lamb, and my rock and my salvation." (1Nephi 13: 35-36)
The work of the Lord in the latter days is multi-faceted but centers in the House of Israel. His primary purposes are: To gather scattered Israel. (1Nephi 10: 14) To fulfill His promises to the fathers of Israel. (1Nephi 22: 6-11) And to prepare a people from among gathered Israel to receive Him at the time of His return to reign. (3Nephi 21: 23-25 and Ether 13: 10-12) The Lord's plan for the latter days is all about the house of Israel and fulfilling His promises to them and their fathers. The Gentiles are to facilitate the bringing forth of the knowledge that will bless latter day Israel to accomplish the Lord's purposes.
Nephi explained to his brothers the role of the latter day Gentiles in bringing their future seed to a knowledge of the Redeemer and His gospel.
"And now, the thing which our father meaneth concerning the grafting in of the natural branches through the fullness of the Gentiles, is, that in the latter days, when our seed shall have dwindled in unbelief, yea, for the space of many years, and many generations after the Messiah shall be manifested in body unto the children of men, then shall the fullness of the gospel of the Messiah come unto the Gentiles, and from the Gentiles unto the remnant of our seed— And at that day shall the remnant of our seed know that they are of the house of Israel, and that they are the covenant people of the Lord; and then shall they know and come to the knowledge of their forefathers, and also to the knowledge of the gospel of their Redeemer, which was ministered unto their fathers by him; wherefore, they shall come to the knowledge of their Redeemer and the very points of his doctrine, that they may know how to come unto him and be saved." (1Nephi 15: 13-14)
The Gentiles play a major supporting role in the Lord's plan for Israel, but it is only a supporting role. The Gentiles are not, and do not become, the house of Israel. The designation and identification of "Gentiles" is maintained separate from the remnant, (or remnants,) of the house of Israel throughout the Book of Mormon narrative. The Gentiles may be "numbered among" the house of Israel (3Nephi 16: 12-14, and 3Nephi 21: 6 and 2Nephi 10: 18-19 and 3Nephi 21: 22) if they are willing to repent and come unto the Lord. However, being "numbered among" is not the same thing as "being" the remnant blood of Israel with its specific promises of the Lord.
The identifying designation of the primarily European bloodlines on the American continent as "Gentile" in the Book of Mormon is no different than the designation of "Gentile" converts to the meridian day church as "the brethren which are of the Gentiles." (Acts 15: 23) Though baptized and converted to the gospel and the Meridian Day Church of Christ, the Gentile converts continued to be identified by Peter and James, as "the brethren which are of the Gentiles." In the very same way, the Gentile immigrants of European descent to this continent, and their offspring, are identified throughout the Book of Mormon narrative as "Gentiles." (D&C 109: 60)
Joseph Smith was the latter day Gentile prophet called by the Lord to bring forth the Book of Mormon and the gospel of Jesus Christ in the latter days. Nephi, speaking of his seed, (the remnant of Israel,) said,
And after our seed is scattered the Lord God will proceed to do a marvelous work among the Gentiles, which shall be of great worth unto our seed; wherefore, it is likened unto their being nourished by the Gentiles and being carried in their arms and upon their shoulders. And it shall also be of worth unto the Gentiles; and not only unto the Gentiles but unto all the house of Israel, unto the making known of the covenants of the Father of heaven unto Abraham, saying: In thy seed shall all the kindreds of the earth be blessed." (1Nephi 22: 8-9) Later in the record, Nephi observes, "And the things which shall be written out of the book (of Mormon) shall be of great worth unto the children of men, and especially unto our seed, which is a remnant of the house of Israel. (2Nephi 28: 2)
The restoration of the gospel of Jesus Christ and the bringing forth of the Book of Mormon by the Gentile prophet Joseph Smith in the latter days, has the primary purpose of bringing forth the gospel of Jesus Christ to the remnant of Israel. The restoration "shall be of great worth unto our (the Nephite/Lamanite) seed; wherefore, it is likened unto their (the remnant of Israel) being nourished by the Gentiles and being carried in their arms and upon their shoulders." The Gentiles themselves and all the house of Israel will also be blessed by the truths and gospel restored by Joseph Smith.
Why did the Lord appoint the Gentiles to play such a prominent and important role affecting the destiny of the house of Israel, the Lord's people? This is according to the prophecy spoken by many prophets that describes the movement of primary stewardship for the gospel of Christ. In his great vision of the history and future of the world, Nephi was told:
"And the time cometh that he shall manifest himself unto all nations, both unto the Jews and also unto the Gentiles; and after he has manifested himself unto the Jews and also unto the Gentiles, then he shall manifest himself unto the Gentiles and also unto the Jews, and the last shall be first, and the first shall be last." (1Nephi 13: 42)
The gospel of Christ has now moved to the third of the stewardship designations identified in the outlined progression. The Lord has now manifested Himself to the latter day Gentiles. The role of the Gentiles will be fulfilled. The fullness of the Gentiles has come and will pass away. The remnant of Israel (the Jews and all Israel) will have the final manifestation of the Lord and the final responsibility as stewards of the gospel of Jesus Christ. At the end, the last to receive the manifestation of the Lord will be the first. Israel will be prepared for the coming of their King.
And then cometh the New Jerusalem; and blessed are they who dwell therein, for it is they whose garments are white through the blood of the Lamb; and they are they who are numbered among the remnant of the seed of Joseph, who were of the house of Israel. And then also cometh the Jerusalem of old; and the inhabitants thereof, blessed are they, for they have been washed in the blood of the Lamb; and they are they who were scattered and gathered in from the four quarters of the earth, and from the north countries, and are partakers of the fulfilling of the covenant which God made with their father, Abraham. And when these things come, bringeth to pass the scripture which saith, there are they who were first, who shall be last; and there are they who were last, who shall be first. (Ether 13: 10-12)