It's likely that Joseph included the KJV passages in the Book of Mormon because he believed they effectively conveyed the applicable verses he encountered during the revelatory translation process.

The Book of Mormon was "given after the manner of their language," as the Lord tells us in D&C 1:24. This means that the text was written in Joseph's words and in a way that would resonate with his audience. At the time, the King James Bible was the primary spiritual language, so it's likely that this style spoke to Joseph and his contemporaries.

As part of the translation process, the Lord commanded Joseph to "study it out" in his mind, as we see in D&C 8. This implies Jospeh carefully considered his word choices and other aspects of the translation, suggesting that the inclusion of KJV passages was a deliberate choice rather than mere copying or plagiarism.

Author Stephen Gibson suggests:

"instances where the Book of Mormon parallels the Bible, Joseph Smith must have noted the parallels and used the King James Bible to guide him in his choice of words. If the Book of Mormon agreed with the Biblical text in meaning, he apparently utilized the Biblical text, italicized words and all. However, when the plates differed from the Biblical text, he followed the text on the plates. For example, of 433 verses of Isaiah quoted in the Book of Mormon, 46 percent are identical to those in the Bible, while 54 percent are modified to some extent.” It should be noted, however, that none of those contemporaries involved in the translation process recall Joseph consulting the Bible or any manuscripts.

Translation was Actually Revelation

This will be addressed more elsewhere. It's a fact that Joseph didn't sit at his desk with a reformed Egyptian lexicon and matching characters and deriving translations. A reformed Egyptian lexicon didn't even exist. The Book of Mormon was revealed by the “gift and power of God." That's the only description Joseph gave of the translation process.

Other Considerations

There are numerous accounts by those involved in the translation that say Joseph didn't access any manuscripts. So how do we reconcile those accounts with the clear examples of KJV in the Book of Mormon? It's hard to know but it seems as if they might have been wrong. Some have sought to reconcile the statements by speculating that God might have touched Joseph's memory to share the KJV passages that he had once read. Perhaps, but it's all conjecture.

There is some debate about a "tight" versus "loose" translation. Those arguing for a tight translation often look to two Book of Mormon witness statements in particular. David Whitmer & Martin Harris.