I suppose this idea has spread because of the Savior’s declaration on the Mount of Olives: “And again, this Gospel of the Kingdom shall be preached in all the world, for a witness unto all nations, and then shall the end come, or the destruction of the wicked” (Joseph Smith-Matthew 1:31).
Elsewhere we read that “the sound must go forth from this place into all the world, and unto the uttermost parts of the earth—the gospel must be preached unto every creature, with signs following them that believe” (D&C 58:64).
Yes, every man and woman who comes to planet earth will have an opportunity to hear and receive the fullness of the gospel, in his or her own tongue (D&C 90:11). But we all know that many of our Father’s children do not have that opportunity in this life; hence the powerful and expansive work of preaching the gospel that is going forward beyond the veil of death in the spirit world (D&C 138).
In addition, the work of gathering—which is really missionary work, the process by which the people of the earth are gathered to Christ, his gospel, his doctrine, his Church, and to the congregations of the faithful (see 1 Nephi 15:13-15; 2 Nephi 6:10-11; 9:1-2; 10:7-8)— will go forward in the great Millennium, after his coming in glory. This gathering will be of such a magnitude as to cause all previous gatherings to almost fade into insignificance (see Jeremiah 16:14-17; 1 Nephi 22:24-25; 2 Nephi 9:2; 30:6-18; 3 Nephi 21:25-26). All will hear, to be sure, but not necessarily before the Master returns.