You are correct that denominations will never represent the one faith and one doctrine required of the one church as proscribed in scripture.
"It comes down to authority" this was the first hit on Google for that phrase with lds appended. A quick way to learn the pros and cons of an idea from a lds perspective.
... There are understandable justifications for individuals who choose to leave the church ... This post is not meant to be an attack on those who don’t believe in the church but rather simply my testimony as to why I believe it to be true.
So with all this being said, let me start with just a couple of reasons of why I still believe the way I do.
The Strength of Our Position
... Many years ago there came to Salt Lake City a learned doctor of divinity, a member of the Roman Catholic Church. I became well acquainted with him, and we conversed freely and frankly. A great scholar, with perhaps a dozen, languages at his tongue’s end, he seemed to know all about theology, law, literature, science and philosophy, and was never weary of displaying his vast erudition. One day he said to me: “You Mormons are all ignoramuses. You don’t even know the strength of your own position.
It is so strong that there is only one other tenable in the whole Christian world, and that is the position of the Catholic Church. The issue is between Catholicism and Mormonism. If we are right, you are wrong; if you are right, we are wrong; and that’s all there is to it.
The Protestants haven’t a leg to stand on. If we are wrong, they are wrong with us, for they were a part of us and went out from us; while if we are right, they are apostates whom we cut off long ago. If we really have, as we claim, the apostolic succession from St. Peter, there was no need for Joseph Smith and Mormonism; but if we have not that succession, then such a man as Joseph Smith was necessary, and Mormonism’s attitude is the only consistent one. It is either the perpetuation of the Gospel from ancient times, or the restoration of the Gospel in latter days.”
It really is one or the other when it comes down to authority. It either continued through the apostles to the modern day or it was lost when they died and thus a restoration of those keys was needed to restore the gospel in our day. This idea or notion of the need to have the gospel restored is such a crucial aspect to Mormon theology. It either happened or it didn’t.
What Happened to the Billions of Individuals Who Died Not Ever Hearing About Christ?
So we know that Christ Himself taught that He was “the way, the truth, and the life: no man cometh unto the Father, but by me.” (John 14:6.) If this premise is true and we know that baptism is an essential ordinance that one must receive in order to receive salvation, what happens to all those who died never being baptized? What happens to the billions of individuals who have never heard about Christ. ...
http://www.ldssmile.com/2014/07/01/strength-position/
I included the last bit to show our Heavenly Father didn't just abandon Gandhi and everyone who has or will die without the opportunity to hear the gospel.