Well you have to accept that Peter James and john waited over 1800 years and then came to earth as resurected beings and ordained them in secret with no other witnesses. That’s a bit more of a stretch than the documented succession of bishops in the Catholic Church.
They waited 1800 years until the winter of apostasy had past and the children of God were ripe for the Gospel. It required the right time (age of enlightenment), the right place (a land of religious liberty), and the right person (the foreordained prophet, a 14 year old boy of honest faith seeking the true Church of Christ.)
“Then came that period known as the Renaissance, which gave to men an inward longing for liberation of thought with the courage to face the evil forces that held them in subjection. Man again began to seek for freedom and truth. The Master of men had said many years before, “… ye shall know the truth, and the truth shall make you free.” (John 8:32.) But this and other scripture, for many years, they had not even been privileged to read.
But God began to work with men, and their hearts turned toward him; and whenever the spark of freedom was found, it was influenced and fed by the natural forces of agency. Soon the desire for freedom, matched with the courage to fight and die for it, spread among men.
The question might well be asked, Why does freedom need to be restored as a forerunner to a new dispensation of the gospel of Jesus Christ? The answer is a simple one, for well the Lord knows that without the spirit of freedom in the souls of men, there could be no willing response to the gospel plan. For it is in the culture of freedom and the use of agency in that freedom that men come to know the difference between good and evil. This progress leads to yearnings in the hearts of good men, and eventually to gospel dispensations. This is the pattern to be noted down through the era of the historical writings.
The continued longing for freedom led directly to the period known as the Reformation, which led to the foundation of America and the framing of the Constitution, concerning which the Lord has said:
“According to the laws and constitution of the people, which I have suffered to be established, and should be maintained for the rights and protection of all flesh, according to just and holy principles.” (D&C 101:77.)
All of this in its proper order leads directly to the greatest period in the experience of man upon the earth, a new dispensation of the gospel of Jesus Christ.
This period was foreseen and referred to by the apostle Peter as the times of restitution or restoration of all things involving a new gospel dispensation. Here are his words as he speaks also of the coming of the Lord at this particular time:
“And he shall send Jesus Christ, which before was preached unto you:
“Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.” (Acts 3:20–21.)
Alvin R. Dyer, “The Last Dispensation,” Ensign, July 1972, 52
“As a young man, Joseph “was called up to serious reflection” on the subject of religion. Because he was born in a land of religious freedom, he could question which of all the churches was right. And because the Bible had been translated into English, he could seek an answer from the word of God. He read in the book of James, “If any of you lack wisdom, let him ask of God,” and he did as directed. In answer to Joseph’s prayer, God the Father and His Son, Jesus Christ, appeared to him. This humble farm boy was the prophet chosen by God to restore the ancient Church of Jesus Christ and His priesthood in these latter days.”
Robert D. Hales, “Preparations for the Restoration and the Second Coming: ‘My Hand Shall Be over Thee,’ ” Ensign, Nov. 2005, 88