The problem is is that the LDS religion is usurping the place of the Holy Spirit. It is the Spirit's job to guide is to all understanding, to open our minds to the will of the Father, to help us be conformed to the image of the Son. It is not the religion's place at all to "produce the faith necessary [to lead] unto life and salvation". God produces that faith. God is the author and finisher of our faith. He creates it and He completes it. Any faith that is produced by any other person/organization/object only produces faith in that person/organization/object. None of it is salvific.
There is true religion, and there is man made religion. We agree that the Holy Spirit is the only Source to know the difference. We all must discover that Source. Jesus made that possible by teaching His disciples how it is done, and ordained them to teach others. He organized a Church that was based on their leadership, and equipped them with the gifts of the Spirit, including revelation, to compensate for their personal human weakness. The apostles were imperfect, but followed the Savior's instructions as they themselves learned to overcome the world. Following them, and giving heed to their counsels would bring us to the understandings by the Spirit, including this: James 1:27 "Pure religion and undefiled before God and the Father is this, To visit the fatherless and widows in their affliction, and to keep himself unspotted from the world." Service and sacrifice in the name of pure religion.
How many examples do we find where the apostles encountered hearts among the followers that could not perceive their message? Why did God not produce the faith among them? It was not God that failed them. People today seem to believe that God changes people by some method of removing the bad parts and installing the new ones. If that is what it takes, why did He not install the correct parts in the first place? It was, is, and always will be the people failing God by not embracing and putting into practice the package presented to them called the Gospel of Jesus Christ. That is His religion, and obedience to its precepts is what changes us. That is how God changes us.
We learn faith by embracing and obeying the truths revealed by God, that we actually do not understand at first. It is given in the form of milk as our faith begins to increase. It takes faith to go from step to step, so faith is exercised and grows. Many do not get past this early development stage, as illustrated in Hebrews 5 and several other examples in scripture.
You are absolutely correct when you say: "Any faith that is produced by any other person/organization/object only produces faith in that person/organization/object." That has been the downfall of mankind since the apostles were killed, and eventually the Church of Rome absorbed the name of Christianity. And every division since is simply another person/organization/object that produces another man made faith. Those are non-salvific, because what Jesus first organized and established was no longer established ..... temporarily. The gates of hell would not prevail, even though it made its attempt, and evil was exposed. "...The restoration of all things" was always part of the plan to prevail.
"Pure religion" was restored. Its validity is not perceived until a seeker goes through the "milk stages" as described above. And it is easy to mock and find fault because of the imperfect people that God has called to restore it, and even to administrate the affairs currently. No different than before. God has equipped those whom He called with gifts of the Spirit, including revelation, to compensate for their weaknesses. If that was not the case, this Restored Church and Gospel would never have survived the first few years. It is the "stone cut out of the mountain without hands, and is filling the earth, a prophecy that must be fulfilled before the coming of Christ.
I do not believe there is a "religion" that better exemplifies and practices the art of "pure religion" by serving the fatherless and widows, and inspires its members to " keep himself unspotted from the world" than this Restored Church of Jesus Christ. It demands much of us, yes. But that is God's gift to us for the development of faith.