When Nephi wrote these passages, he was without his father. Nephi would have rejoiced in knowing that there is a plan, that the covenant of the Lord was still firm, that his arm was outstretched, that his people were not going to be forgotten, and that even the isles of the sea would not be ignored. Think about being desperately in need of that kind of comfort. We can see why these texts of Isaiah would have meant the world to Nephi.
Book of Mormon Central, "Why is the Lord’s Hand ‘Stretched Out Still’? (2 Nephi 19:12)," KnoWhy 49 (March 8, 2016).