“And he [Benjamin] also taught them concerning the records which were engraven on the plates of brass, saying: My sons, I would that ye should remember that were it not for these plates, which contain these records and these commandments, we must have suffered in ignorance, even at this present time, not knowing the mysteries of God. For it were not possible that our father, Lehi, could have remembered all these things, to have taught them to his children, except it were for the help of these plates; for he having been taught in the language of the Egyptians therefore he could read these engravings, and teach them to his children, that thereby they could teach them to their children, and so fulfilling the commandments of God, even down to this present time. I say unto you, my sons, were it not for these things, which have been kept and preserved by the hand of God, that we might read and understand of his mysteries, and have his commandments always before our eyes, that even our fathers would have dwindled in unbelief, and we should have been like unto our brethren, the Lamanites, who know nothing concerning these things, or even do not believe them when they are taught them, because of the traditions of their fathers, which are not correct.” (Mosiah 1:3-5).
From the above verses it is clear that the the brass plates were written in “the language of the Egyptians” (the “language of the Egyptians”, however, is a broad and ambiguous statement, which I will not address here). This is why the gold plates were also in Egyptian – their model was the brass plates, which were in that language (some form of Egyptian language). Why were sacred texts of the Jews in this language? It comes down to the fact that it was more efficient than Hebrew was for writing with limited space. Making golden plates appropriate for archival writing was also a difficult process. In essence, the script that they wrote in was a type of shorthand and one patterned off the language on the plates of brass (but likely changed over time). It’s also likely that the writing was an Egyptian script transliteration of Hebrew (or some variant of Hebrew over time).
“And now, behold, we have written this record according to our knowledge, in the characters which are called among us the reformed Egyptian, being handed down and altered by us, according to our manner of speech. And if our plates had been sufficiently large we should have written in Hebrew; but the Hebrew hath been altered by us also; and if we could have written in Hebrew, behold, ye would have had no imperfection in our record. But the Lord knoweth the things which we have written, and also that none other people knoweth our language; and because that none other people knoweth our language, therefore he hath prepared means for the interpretation thereof.” (Mormon 9:32-34).
Egyptian was an international language of the time. Israel was part of a large eastern Mediterranean trading circuit at the time with a lot of trading and travel in particular between Jerusalem and Egypt. Lehi knew Egyptian and so knowledge of the language was passed down through the generations, although the script and language were modified over the 1000 year span of the main story of the Book of Mormon. This means that the writing on the small plates of Nephi that Mormon included with his abridgment of the larger plates of Nephi, while readable to Mormon, was not necessarily the same script as he used for the rest of the plates (just as Old English is readable to those knowledgeable but qualitatively different from modern English).
What’s also clear from this passage about the language of the Book of Mormon is that “none other people knoweth our language”, meaning just what that sounds like – the particular language that the Nephites developed over time was unknown to anyone else in the world (and still is – well, except for the 3 Nephites). Further, the language used to keep records of the people and prophecies was not the main language that most of the Nephites spoke, at least over time as the civilization expanded. The language of the records (and possibly just those kept on metal plates) was a special language taught to those who would have responsibility for keeping the records. For example, “I, Zeniff, having been taught in all the language of the Nephites” (Mosiah 9:1; emphasis added). We have to remember that the Nephites were a small group of people who lived in a fairly discrete area of the Americas. There were always more Lamanites than Nephites (both terms are political and do not necessarily denote ancestry, race, or ethnicity), likely in part because there were other peoples in the Americas with whom the Lamanites mixed (the original Nephites originally might not because that would mean marrying non-covenant people but the term Nephite became more inclusive over time to include many who were not church members). In general though, both groups were small relative to the overall population of the Americas. This is evident in the fact that the Mulekites were living nearby for hundreds of years but were not seen (or at least commented on by the records we have from Mormon) until the time of Mosiah. Also, the Jaredites were nearby (in the last years of their civilization) but did not have much interaction with the other Book of Mormon groups. The Nephites might have had contact with other peoples but such records were not included in the Book of Mormon because they are not relevant in a book of scripture.
After that aside, I’ll return to languages. Languages change quickly, particularly when not written down and maintained. For example, another group of people came out of Jerusalem shortly after Lehi left, arriving at a different part of the Americas: “Behold, it came to pass that Mosiah discovered that the people of Zarahemla came out from Jerusalem at the time that Zedekiah, king of Judah, was carried away captive into Babylon. And they journeyed in the wilderness, and were brought by the hand of the Lord across the great waters, into the land where Mosiah discovered them; and they had dwelt there from that time forth. And at the time that Mosiah discovered them, they had become exceedingly numerous. Nevertheless, they had had many wars and serious contentions, and had fallen by the sword from time to time; and their language had become corrupted; and they had brought no records with them; and they denied the being of their Creator; and Mosiah, nor the people of Mosiah, could understand them. But it came to pass that Mosiah caused that they should be taught in his language. And it came to pass that after they were taught in the language of Mosiah, Zarahemla gave a genealogy of his fathers, according to his memory; and they are written, but not in these plates [small plates of Nephi].” (Omni 1:15-18; emphasis added).
Much of the teaching of language by Lehi, Nephi, and on through the generations was to not only maintain the language but also to maintain culture. However, most importantly, it was to maintain the ability to read the scriptures and thus encourage faith in God.
So, in closing and to summarize, the gold plates of Mormon that Joseph Smith translated were written in their “reformed Egyptian” script because that’s what the brass plates were written in (or at least the brass plates were a previous iteration of the particular script used on the gold plates). We don’t really know why the brass plates were in that language (Egyptian – some form of it but not the “reformed Egyptian” of the Book of Mormon). We’ll have to leave that answer until the future.