The 3 Nephi text changes the focus away from the temple and toward the Savior. In the New World, the people appear to have had readier access to the temple and fewer purity restrictions than in the Old World. Furthermore, the Messiah is standing before them. The risen Savior is the Lord of the temple and its rites, so it is quite appropriate that his presence, not the physical building, would be the focus.
These changes confirm Joseph’s interactions with the King James Version. There is a rather artful blending of insertions, deletions, and retentions in verse 24 to retain as much as possible of the King James Version verse structure while still making desired changes.