Actually, Book of Mormon scholars would never say there was never a Mormon Church. Let's see what some of their doctrines, leadership, practices, and organization.
Intrduction
We find churches named after where they met.
1 Corinthians 1:2 Unto the church of God which is at Corinth
The members there were called Corinthians: 2 Corinthians 6:11 O ye Corinthians, our mouth is open unto you, our heart is enlarged.
Galatians 1:2 And all the brethren which are with me, unto the churches of Galatia: They were called Galatians: Galatians 3:1 O FOOLISH Galatians, who hath bewitched you,
Philippians 1:1 PAUL and Timotheus, the servants of Jesus Christ, to all the saints in Christ Jesus which are at Philippi They were called Philippians: Philippians 4:15 Now ye Philippians know also, that in the beginning of the gospel,
1 Thessalonians 1:1 PAUL, and Silvanus, and Timotheus, unto the church of the Thessalonians which is in God. We see that they were called Thessalonians
There was a church of the Mormons after this naming technique. The Propet Mormon,when talking about the origin of his name,
3 Nephi 5:12 And behold, I am called Mormon, being called after the land of Mormon, the land in which Alma did establish the church among the people, yea, the first church which was established among them after their transgression.
He, of course, is refering to the Church that Alma established in the Land of Mormon.
Mosiah 25:18 Therefore, Alma did go forth into the water and did baptize them; yea, he did baptize them after the manner he did his brethren in the waters of Mormon; yea, and as many as he did baptize did belong to the church of God; and this because of their belief on the words of Alma.
Alma 5:3 I, Alma, having been consecrated by my father, Alma, to be a high priest over the church of God, he having power and authority from God to do these things, behold, I say unto you that he began to establish a church in the land which was in the borders of Nephi; yea, the land which was called the land of Mormon; yea, and he did baptize his brethren in the waters of Mormon.
As you can see, there really was a Mormon Church. The full name may have been called the Church of God of the Mormons.

The Doctrine of the Mormon Church as Opposed to that of the Latter-day Saints

The Latter-day Saints are based on the teachings of Joseph Smith and subsequest Living Oracles. The Mormon Church, according to Alma its founder, was based on the teachings of Abinadi.
Alma 5:11. Behold, I can tell you--did not my father Alma believe in the words which were delivered by the mouth of Abinadi? And was he not a holy prophet? Did he not speak the words of God, and my father Alma believe them?
12. And according to his faith there was a mighty change wrought in his heart. Behold I say unto you that this is all true.
There is a wide difference between the Mormon Church doctrine and the Latter-day Saints doctrine.
Abinadi asks, "Behold, I say unto you, that when his soul has been made an offering for sin he shall see his seed. And now what say ye? And who shall be his seed?"
Latter-day Saints would tell you that we all children of God or we are all His seed. The quote Acts 17:29: "Forasmuch then as we are the offspring of God" and Malachi 2:10 "Have we not all one father? hath not one God created us?". Of course, their doctrine that we are all the literal children of God concieved in a pre-mortal existance comes mostly from their Living Oracles, they will wrest the cited verses to fit their narative to gain some credibiblity as they present their doctrine.
However, the Mormon Church, based on the teachings of Abinadi, would identify those who are considered His Seed and who aren't.
And who shall be his seed?
Behold I say unto you, that whosoever has heard the words of the prophets, yea, all the holy prophets who have prophesied concerning the coming of the Lord--I say unto you, that all those who have hearkened unto their words, and believed that the Lord would redeem his people, and have looked forward to that day for a remission of their sins, I say unto you, that these are his seed, or they are the heirs of the kingdom of God.
For these are they whose sins he has borne; these are they for whom he has died, to redeem them from their transgressions. And now, are they not his seed?
Alma, based on Abinadi, goes on to teach in Alma 5:41 ....whosoever bringeth forth evil works, the same becometh a child of the devil, for he hearkeneth unto his voice, and doth follow him.
In the Mormon Church, the Mormons were taught that we BECOME children of God Mosiah 18:22....And thus they became the children of God. To Abinadi and, therefore Alma and the Mormon Church believed that a person can be a child of the devil.
Jesus died for His seed, His adopted children
For these are they whose sins he has borne; these are they for whom he has died, to redeem them from their transgressions. And now, are they not his seed?
Latter-day saints' doctine is that Father's loving plan that God will save all the works of His hands. The Mormon Church taught that this simply is not true. In fact, they taught, based on the teachings of Abinadi, God, who is also just, CAN NOT (strong words) save all the works of His hands:
But behold, and fear, and tremble before God, for ye ought to tremble; for the Lord redeemeth none such that rebel against him and die in their sins; yea, even all those that have perished in their sins ever since the world began, that have wilfully rebelled against God, that have known the commandments of God, and would not keep them; these are they that have no part in the first resurrection.
Therefore ought ye not to tremble? For salvation cometh to none such; for the Lord hath redeemed none such; yea, neither can the Lord redeem such; for he cannot deny himself; for he cannot deny justice when it has its claim.
The Latter-day Saints teach that even the worse people will be redeemed and then glorified in the Kingdom of God and will be happy beyond comphrehension. Based on the words of Abinadi, the Mormon Church did not recognize this teaching:
And then shall the wicked be cast out, and they shall have cause to howl, and weep, and wail, and gnash their teeth; and this because they would not hearken unto the voice of the Lord; therefore the Lord redeemeth them not....But remember that he that persists in his own carnal nature, and goes on in the ways of sin and rebellion against God, remaineth in his fallen state and the devil hath all power over him. Therefore, he is as though there was no redemption made, being an enemy to God; and also is the devil an enemy to God.
The Latter-day saints teach that there are three+ eternal places that the dead can enter, being glorifed. The Mormon Church taught that there were only two places of destination.
If they be good, to the resurrection of endless life and happiness; and if they be evil, to the resurrection of endless damnation, being delivered up to the devil, who hath subjected them, which is damnation--
The Latter-day saints, like the Catholic bretren, teach that an unrepentant sinner who died in their sins can suffer for their own sins. The Mormon Church would insist that "only in and through Christ ye can be saved?"

LDSaints emphisize the Loving God. Hence they can teach that He has a "Loving Plan" which, basically concludes, God saves all the works of His hands. They basically parrot The Book of Mormon False Prophet Nehor.

Alma 1:4 And he also testified unto the people that all mankind should be saved at the last day, and that they need not fear nor tremble, but that they might lift up their heads and rejoice; for the Lord had created all men, and had also redeemed all men; and, in the end, all men should have eternal life.

The Mormon Church, based on the teachings of Abinadi, taught the Loveingness of God in proper propotion so that nobody would be led waswy into carnal security, thinking they will be saved simply because God is loving. Abinadi, instead, taught that God is a Jealous God.

Mosiah 11:22 And it shall come to pass that they shall know that I am the Lord their God, and am a jealous God, visiting the iniquities of my people.

He also taught that God is a Just God. Even the LDSaint is supposed to believe Doctrine and Covenants 1:31 "For I the Lord cannot look upon sin with the least degree of allowance".

Mosiah 15:27 Therefore ought ye not to tremble? For salvation cometh to none such; for the Lord hath redeemed none such; yea, neither can the Lord redeem such; for he cannot deny himself; for he cannot deny justice when it has its claim.

By distorting the teachings of the Mormon Church the Latter-day Saints have created a false God that is just such a big bundle of love that he will save all the works of His hands, even those who die in their sins, were rebels al their lives, who, in summery, lived enemies of God.

We can see that there is quite a difference between the doctrine of the Mormon Church and the Latter-day Saints.

Organization

There is a big difference between the Church of the Latter-day Saints and the Mormon Church.
The LDSaints organiaation is based on Prophets and Apostles. There are in their church 15 apostles,three of them make up the presidency of the church and one of the three is the prophet. They also have a quorum of the seventy. The Mormon Church had a High Priest (not like the one in the Old Testament) and, in each congregation limited to fifty people, there were called to be a Priest and a Teacher.
Mosiah 18:18 And it came to pass that Alma, having authority from God, ordained priests; even one priest to every fifty of their number did he ordain to preach unto them, and to teach them concerning the things pertaining to the kingdom of God.
Mosiah 23:17 And it came to pass that none received authority to preach or to teach except it were by him from God. Therefore he consecrated all their priests and all their teachers; and none were consecrated except they were just men.
Authority of the Church Leaders
The Latter-day Saints claim to have gotten their authority through visitations of angels and resuurected beings and that it has been passed down through the years from leader to leader until today. The Mormon Church, in the Land of Mormon, made no such claim in regards to their authority. Instead, their authority came by the Spirit of the Lord, the Holy Ghost.
Mosiah 18:12. And now it came to pass that Alma took Helam, he being one of the first, and went and stood forth in the water, and cried, saying: O Lord, pour out thy Spirit upon thy servant, that he may do this work with holiness of heart.
13. And when he had said these words, the Spirit of the Lord was upon him, and he said: Helam, I baptize thee, having authority from the Almighty God....
Having that authority through the Spirit of the Lord, again, Mosiah 18:18. And it came to pass that Alma, having authority from God, ordained priests. We see that they did not ordained by some priesthood given by angels, but ordained priest by the same authority that Alma got from the Holy Ghost.
Moroni 3:4 And after this manner did they ordain priests and teachers, according to the gifts and callings of God unto men; and they ordained them by the power of the Holy Ghost, which was in them.
We see that Abinadi spoke with authority from the same origin.
Mosiah 13:5. ....the Spirit of the Lord was upon him....6. And he spake with power and authority from God;
Leaders
The Latter-day Saints revere their leaders to the degree that, to them, the written scriptures mean nothing to them next to their priesthood leaders. In meetings and conferences, they set them above the heads of the congregation. To critisize these leaders is considered apostacy. As they enter or leave a room, the congregations stands in relevant silance until they are seated or are gone.
The Mormon Church had a different attitude towards their leaders.
Alma 1:26 ....the priest, not esteeming himself above his hearers, for the preacher was no better than the hearer, neither was the teacher any better than the learner; and thus they were all equal...
Critisizing leaders, or adminishing them, was something that was expected and this was pointed out to be a wonderful feature of the Mormon Church. Mosiah 26:39 And they did admonish their brethren; and they were also admonished, every one by the word of God, according to his sins, or to the sins which he had committed....
Conclusion
Seeing how lengthy this comparison has grown to, I will close. But there was a Mormon Church. The Book of Mormon, when it bursts on the world, will be seen as the restoration of the gospel in its simplicity and truth. When that takes place, the church of the lamb of God will resemble more the Mormon Church than the LDSaints.