Textual analysis: Verse 7 shifts Nephi's focus from the plates to the true subject matter of his discourse, which is the Savior. At this point of transition it is interesting to speculate on all of chapter 19's role as a transitional section.
Prior to the discussion of the plates, Nephi was involved in a historically framed narrative, where the timeline of events structured both the details and the elaborations of the spiritual implications/revelations that occurred during those chronological events. This framework for Nephi's writings appears to culminate in the arrival in the new world and the finding of the ore, which we have noted leads directly to the discussion of the creation of both the large and small plates of Nephi (and in particular the discussion of this specific set - the small plates).
From this point on in Nephi's writings, there is a shift in the conceptual framework he works with. While the earlier sections followed loosely a historical/chronological frame, from this point on that chronological framework is much less evident. Certainly events occur in some place in time, but the inclusion of material is not directly related to specific events as was the earlier part (with the very obvious exception of the narrative of Lehi's final blessings).
I suggest a possibility or the shift in the nature of the narrative. Clearly the entire narrative at least up to this point has been written years after the events, and some amount of time after the arrival in the New World. I suggest that at this point in First Nephi we begin to catch up to "real time" in Nephi's writing. This shift in focus appears to bring Nephi into the present, with the specific discussion of the plates he is writing on. This suggests that Nephi's consciousness is now focused on the present rather than past events. Nephi has previously dropped into editorial asides, and this one is perhaps similar, except that it marks the general abandonment of that earlier structural paradigm. From this point on we get significantly less history, and an increasing focus on the spiritual, even to the point of the inclusion of large sections of scripture (a feature absent from the historical section).
Scriptural analysis: There is a weariness in Nephi's voice as he writes this. He has just stated (emphatically, and over two verses) that he writes scriptural things that he deems to be of great value. In verse 7 he notes that his understanding is not universal, and that while he (and others - the generic "some men") deems these things to be of tremendous worth, there are those that disdain them. It is impossible to avoid the mental picture of a Nephi writing of the things that stir his soul, and contrasting them with what must have been one of his greatest sorrows - the spiritual (and political) apostasy of Laman and Lemuel and those that followed them. Perhaps there is just a little of the dim fraternal love in Nephi's shift in terms from the very vivid "trample under their feet" and his own rephrasing to "hearken not to the voice of his counsels." Surely the general effect was the same, but the second appears to have a somewhat lesser dark aspect.
In a short and very personal verse, Nephi sets out the great paradox of the gospel, that for some it is so clear and precious, and for others a point of derision. It has always been so. The individual reaction to the revelation of God's will strikes each person in a different way, depending upon their own spiritual capacity to receive. To those prepared it is precious. To those who have chosen to believe in a different voice, the light is painful, and therefore something to attack - in Nephi's words, to "trample under their feet."