I don't draw the straight-line connection between a testimony of the Book of Mormon and an automatic acceptance of all other truth claims of the LDS Church that some members of the Church do, especially onward in time all the way to our day. There are way too many other factors that theoretically could come into play and break such a chain of logic. I think there is a direct link to the Book of Mormon being an inspired recording of the word of God, exactly as we view the Bible in that regard (where inerrancy of the text is not required) and Joseph Smith being a prophet of God, exactly as we view Biblical prophets - but everything else doesn't have that direct correlation, imo. After all, there are prophets who recorded the word of God but didn't establish new churches. In fact, those that did were the very small minority, especially within Judeo-Christian history. Most prophets are more like our modern prophets - caretakers more than radically innovative establishers.
However, I think we miss the real power of the Book of Mormon (the reason it is the keystone of our religion) when we have people read selected verses and passages to prove doctrine and fail to ask them to approach it as it asks to be approached - even if we insert the First Vision as the new keystone of our religion. I don't see anywhere in the Book of Mormon that says, internally, in the words of the authors and abridgers, to use it as a doctrinal proof-text - especially by isolating and emphasizing specific verses and doctrines. What it asks internally - what the words themselves ask - is that the book be read in its entirety in order to open the reader's mind to the reality that God has worked with people throughout history and, therefore, will speak directly to her and manifest truth to her.
When I attended Seminary, one of our Scripture Mastery passages was Moroni 10:3-5. Now, as my children go through Seminary, the passage is only Moroni 10:4-5. I think that is a shame, since it is 10:3 that sets the stage for 10:4-5. Teaching Moroni 10:4-5 without 10:3 is an example of the proof-texting I'm addressing.
Moroni 10:4-5 reads:
"And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost. And by the power of the Holy Ghost ye may know the truth of all things."
That is Moroni's invitation (not a "challenge", which is another personal soapbox) - the "doctrine" of prayer and personal revelation, if you will. It's fine to use that text to teach that doctrine. However, leaving out Moroni 10:3 eliminates entirely a key part of the actual method Moroni is trying to encourage readers to use to go beyond proving doctrine and encounter really deep, meaningful understanding of and communication with God.
Moroni 10:3 reads:
"Behold, I would exhort you that when ye shall read these things, if it be wisdom in God that ye should read them, that ye would remember how merciful the Lord hath been unto the children of men, from the creation of Adam even down until the time that ye shall receive these things, and ponder it in your hearts."
The proof-text approach "challenges" someone to pray about the Book of Mormon - or, in many cases, to pray about some specific passages from the Book of Mormon - or, in many cases, to pray about everything else the missionaries are teaching. It becomes a very generic:
"Pray about what we are teaching you, including the parts of this book we're quoting as we teach these things".
**That's not what Moroni's actual words exhort people to do.**
Moroni says, "when you shall read these things" - which can be while reading or upon finishing reading the multiple records he and his father abridged into one volume, not a few proof-text passages. Furthermore, 10:3 includes the following prior to 10:4 even asking people to pray:
1) Remember the Lord's mercy throughout time (described for those of Israelite descent explicitly throughout the Book of Mormon and the Bible but, interestingly, also applicable to a Buddhist in Japan or a Muslim in Iraq with regard to their own understanding of God's mercy to their own ancestors);
2) Ponder that mercy.
Moroni 10:3 does NOT say to ponder "these things" (doctrines) in "your mind" (by thinking about them). It says to ponder "it" (God's mercy) in "your heart" (by feeling that mercy settle inside you).
A reader of the Book of Mormon can't have the experience Moroni is urging if the Book of Mormon isn't used as he's urging it to be used. That reader might gain a converting testimony, but it won't be what Moroni is exhorting her to experience in her heart. That is important to me.
A testimony of the First Vision can't provide the experience Moroni is exhorting people to have, either. It is wonderful and a necessary part of the Restoration, but it is fundamentally different than the Book of Mormon.