Why did Joseph Smith state that, "A man would get nearer to God by abiding by its (The Book of Mormon) precepts, than by any other book" ?

It seems to me that the answer begins in the very first verse (1 Nephi 1:1) where Nephi (then a mature man) states, "...having had a great knowledge of the goodness and the mysteries of God...I make a record..."     And not even leaving Chapter 1, he describes how his Father (Hebrew for the calling of a prophet or messenger or mediator) received his calling and election made sure.

The rest of the Book of Mormon then names 30 individuals who likewise achieved that "greatest gift"
and intimates that there were numerous others, 20 of whom received the Second Comforter.

The greatest gift is eternal life or life in the celestial kingdom (D&C 14:7 and the index under Eternal Life).  The Second Comforter is the appearance of the Lord Jesus Christ Himself declaring that a man and wife will be exalted  (see Teachings of the Prophet Joseph Smith pp. 150-151).