Logic
The claim that these teachings would not have existed were it not for Joseph Smith is a textbook example of the logical fallacy known as begging the question.
The claim assumes at the outset that a) Joseph Smith was not a prophet communicating authoritative revelation from God. Absent this assumption, there remains the possibility that b) these teachings really were revealed by God, who could have revealed them to someone other than Joseph Smith had Joseph Smith been unwilling.
If we assume either a or b as a premise, any conclusion that these teachings do/don't come from God is but a case of circular reasoning. The introduction to the Book of Mormon lays out a different order of operations in coming to know the truth of the restored gospel:
Those who gain this divine witness from the Holy Spirit [a testimony of the Book of Mormon] will also come to know by the same power that Jesus Christ is the Savior of the world, that Joseph Smith is His revelator and prophet in these last days, and that The Church of Jesus Christ of Latter-day Saints is the Lord’s kingdom once again established on the earth, preparatory to the Second Coming of the Messiah.
Latter-day Saints are called upon to trust Joseph Smith's prophetic teachings because of the witness of the Holy Ghost, not because of the a priori assumption that the teachings are true.
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Historical literacy
For sake of clarity, I will refer to the following as the Texts of the Restoration1:
Although Joseph Smith contributed more to the canon of scripture than anyone else in modern times, he did not author all of the texts of the Restoration.
The men who would become Joseph Smith's first 5 successors (Brigham Young, John Taylor, Wilford Woodruff, Lorenzo Snow, and Joseph F. Smith), his later successor Spencer W. Kimball, as well as David Whitmer and Oliver Cowdery, all authored portions of the Doctrine & Covenants.
Oliver Cowdery also authored a fraction of the Pearl of Great Price.
A few examples, including historical context, can be found here, here, and here.
Thus, as a matter of objective historical fact, it is incorrect to state that Joseph Smith exclusively produced all of the texts of the Restoration.
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Comparison to other scriptural writings
In some cases there are scriptural teachings that we have today only through the record of a single author, but it does not therefore follow that such teachings are untrue. We find this repeatedly in the Bible:
- More than 90% of the Gospel of John is unique to the Gospel of John, including some of the most theologically deep teachings of Jesus' ministry
- All 4 Gospels (even Mark!) contain material not found in any of the other 3.
- The book of Revelation is highly unique compared to the rest of the New Testament
- "thou art Peter, and upon this rock I will build my church" is a statement recorded only by Matthew. This does not mean Matthew's record is untrue.
- Large portions of the Reformers theological arguments derive from teachings recorded by Paul. It does not follow that Paul's record is untrue because there are cases where the same statement was not made by Matthew, Mark, Luke, John, James, Peter, or Jude.
- A whole host of Isaiah's prophecies are unique to him 2
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Ongoing Revelation
We believe all that God has revealed, all that He does now reveal, and we believe that He will yet reveal many great and important things pertaining to the Kingdom of God. (Articles of Faith 1:9)
Latter-day Saints believe that God did not stop speaking when Joseph Smith died any more than He stopped speaking when Moses left this earth. Several examples of teachings/actions of modern prophets, subsequent to Joseph Smith, are reviewed in this post on the site.
Latter-day Saints believe in ongoing revelation and a living prophet who is as much an authorized representative of God as was Moses. Latter-day Saints are not expected to blindly trust in their leaders, but are asked to gain their own divine witness of the truth of the principles taught in the church. Millions attest that they have done so.
My own thoughts on coming to know truth for oneself are described in the latter half of this video.
Disclaimer - these thoughts are products of my own study and do not constitute official statements by The Church of Jesus Christ of Latter-day Saints
1 - "Texts of the Restoration" is not an official term -- I simply use it as a concise descriptor for all 3 volumes together
2 - What a shame it would be if someone listening to Handel's Messiah tried to shout down the choir as heretics, because the prophecy in Isaiah 9 comes to us through the writings of a single person =)