Investigators often ask about the current whereabouts of the golden plates. If Joseph Smith had found an ancient record, it should be displayed like the relics of King Tut, or any other archeological site. What is misunderstood, is that the Book of Mormon was delivered and translated by the power of God. The Lord makes it clear that the sealed portion is not to go forth to the world until it is time, in his infinite wisdom, to reveal all things unto the children of men (v. 22). In order to protect this sealed portion, Joseph Smith was required to return the plates to Moroni when he was done translating the unsealed portion. Even if Joseph had been able to show the plates to the world, they would not have believed his message, Behold if they will not believe my words, they would not believe you, my servant Joseph, if it were possible that you should show them all these things (the plates, etc.) which I have committed unto you (DC 5:7).
Joseph Fielding Smith
"The question has been asked many times of our elders: Where are the plates? Does the Church have in its possession the plates from which the Book of Mormon was translated by Joseph Smith?
"When the answer is given that the plates were received again by the Angel Moroni, who through the centuries since they were hid up unto the Lord has been their special guardian, the reply is generally made: What a wonderful aid it would be to your people in convincing the world of the truth of your story if you could show the plates to prove that Joseph Smith really had them.
"Perhaps it is natural for a man who hears for the first time the story of Joseph Smith and the coming forth of the Book of Mormon to propound such a question and to think that the plates, if they had been placed in some museum where the public could examine them, would have added much to prove the authenticity of the Prophet's story. With deeper reflection we discover that this would not have been the case, for it is not the way the Lord proves his truth, now or at any other time. However, in surprise, and in some cases with an incredulous smile, the propounder of this question turns away feeling that such an answer as he has received is an admission that Joseph Smith never had the plates and practiced a fraud upon the public.
"EXISTENCE OF PLATES WOULD NOT PROVE DIVINITY OF BOOK. It is well in considering this matter to remember the words of the Lord to Isaiah: 'For my thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.'(Isa 55:8)
"If the Lord had followed the thoughts of men and had commanded Joseph Smith to place the plates in some repository where they could have been inspected by the curious public, it would have led to endless disputations. Enemies of the Church would not have been convinced and would have contended most bitterly that the plates were spurious. No one could have read them for the characters engraved on them are unknown to the savants of the present age.
"The Lord does not convince men of his truth by placing before their eyes and in their hands tangible evidence, as a lawyer may do before the court, marking it exhibit A and exhibit B, and then expect it to be accepted. The Lord expects the searcher after truth to approach him with a contrite spirit and with sincerity of purpose; if he will do this and keep the commandments of the Lord, he shall receive the witness through the Holy Spirit and shall know the truth." (Doctrines of Salvation, vol. 3, pp. 227-8)