Why would Joseph Smith frequently use the “periphrastic did” in the Book of Mormon?

The “periphrastic did” is an ancient grammatical form in which the verb “did” is used as an auxiliary verb, such as in 1 Nephi 1:15:

And after this manner was the language of my father in the praising of his God; for his soul did rejoice, and his whole heart was filled, because of the things which he had seen, yea, which the Lord had shown unto him. (emphasis added)

This form is used over 1,700 times in the Book of Mormon in connection with over 400 verbs yet this ancient grammatical form all but vanished sometime in the 1700s.

Stanford Carmack remarks:

Writers cannot manufacture out of thin air vanished forms and lexical meaning when language shift has taken place, thereby obscuring prior usage. That of course is precisely the case of the BofM’s past-tense syntax. High-rate nonemphatic adp did adjacency disappeared before the 18c and was not generally known. So Joseph Smith had no knowledge that it was used at high rates during the 16c and the 17c. (The anomalous use of biblical did eat would not have told him that, just as it does not tell us that today.)
– Stanford Carmack – The Implications of Past-Tense Syntax in the Book of Mormon

How do we account for the high usage of the “periphrastic did” in the Book of Mormon if it reflects Early Modern English more than the Bible?

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