Any scholar of nineteenth-century Mormonism would be well served to read the BOM in its entirety. I should have done so long ago. It would have helped me more fully understand certain terms (such as the Liahona or the Gadiantons). It's one thing to read explanations of such terms. It's another thing to read them in context. And perhaps I'll have some recollection of the narrative when I see artwork about BOM stories or references to BOM figures. I'm trying to gain a better understanding of recent and contemporary Mormonism, and it's worth keeping in mind that the LDS Sunday school curriculum takes members through the BOM in its entirety once every four years. [The other three years are devoted to, respectively, the Old Testament (including the books of Moses and Abraham, which Joseph Smith brought forth in the 1830s), the New Testament, and the Doctrine & Covenants]. Thus, active Latter-day Saints today probably have a much higher level of familiarity with the BOM than their nineteenth-century counterpart.
Of course, if you have a passing interest in things Mormon or teach it occasionally as a subject, it might make more sense to read portions in order to better explain the scripture in class. I've used portions of 1 Nephi, 2 Nephi, and 3 Nephi, and Moroni for that purpose. I also found Ether's account of the Jaredites an interesting case study of the BOM as a whole. It contains an ocean crossing, some interesting points of doctrine (spirit body of Christ, as mentioned above), record keeping, an emphasis upon Jesus Christ, and the extinction of a people.