I have two questions actually for Latter-day Saints:
No.
Having religious truths established through reasoning and proof has never been the Christian way. Jesus said that "A wicked and adulterous generation seeketh after a sign" (Matthew 16: 4), and we've all seen the truth of this, haven't we? Especially if you've spent any time online, you know from experience that well over 9 times out of 10, someone who demands "oh yeah? Prove it!" will never accept any proof offered, no matter how solid.
Jesus further said that that signs shall follow them that believe, (Mark 16:17) not that the signs [evidence] shall come first and establish that belief. And Paul tells us that God gave us his Spirit to guide us, that we should "walk by faith, not by sight." (2 Corinthians 5: 5-7)
Latter-Day Saint doctrine on the subject of establishing belief in the truth of the church stems from the final chapter of the Book of Mormon:
3 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.
4 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.
5 And by the power of the Holy Ghost ye may know the truth of all things.
from Moroni chapter 10
This is the true, solid evidence of religious faith. Millions upon millions of Latter-Day Saints attest to the power of this principle: when you go to God in prayer, asking if this thing that purports to be from Him is true, he does answer. It is a distinctive and unmistakable experience, and once you have received a confirmation of the truth from God, any earthly evidence pales by comparison. People can make mistakes, but the witness of the Holy Ghost is powerful and absolute.
There does exist a wealth of earthly evidence to support the claims made by the church, but signs follow those who believe; those who do not wish to, we see again and again, always contrive some way to not have to accept it.
If a person is rational, honestly interested in the truth, and well-informed (by studying as much of the available evidence as humanly possible), should that person be able to reach the conclusion that Mormonism is true?
Absolutely yes, provided that honest interest in truth includes active faith in Christ; see Moroni 10:4:
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.
All people who have sincere hearts, real intent, and faith in Christ are empowered to learn the truth of the Book of Mormon and of the Restoration of the Priesthood and the Gospel of Jesus Christ in the Church of Jesus Christ of Latter-day Saints, and to gain a testimony of living prophets.
If so, how do Latter-day Saints explain the fact that many individuals, Christians from other denominations included, fail to reach that conclusion?
The Lord Himself answered this question in Doctrine and Covenants 76:75, 79 and 74, Speaking of those who at best do not receive the testimony of His living servants, He says:
These are they who are honorable men of the earth, who were blinded by the craftiness of men. ... These are they who are not valiant in the testimony of Jesus; Who received not the testimony of Jesus in the flesh, but afterwards received it.
Failing to ask in faith or failing to accept a witness given is addressed in Doctrine and Covenants 93:31-32:
Behold, here is the agency of man, and here is the condemnation of man; because that which was from the beginning is plainly manifest unto them, and they receive not the light. And every man whose spirit receiveth not the light is under condemnation.
There never has been, nor will there ever be an exception to Moroni's promise. A person either has sufficient faith and sincerity to obtain a witness from God regarding the truthfulness of the Book of Mormon and the Church of Jesus Christ, or he does not. This is by his own choice alone, and it is the same as the decision to receive the testimony of Jesus here in this life (given the opportunity to receive the Book of Mormon), or not. If he gains a witness, he is at liberty to choose whether to be true to it or not. If he is true to the witness, he is valiant. If he is not true to the witness, he hazards bearing false witness, or taking the Lord's name in vain. God will not be mocked. Therefore in the words of James, "Let him ask in faith, nothing wavering" (James 1:6).
Compare to John 3:19-21:
And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil. For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved. But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.
Those whose deeds are evil do not seek to come into the light. It was for this same reason that the ancient Jews who rejected the testimony of Jesus also pretended to follow the prophets by esteeming and giving lip service only to those who were dead prophets, but missing the Mark of the testimonies given by those prophets, by rejecting the living Prophet (see John 8, Matthew 23:29-34).
Not yet knowing what is true is of course not a blanket condemnation. As John and the Lord both attest, condemnation is only a possibility after one has had opportunity to receive light, but has refused it. Thus far there are many who have not yet had that opportunity, so the existence of persons who do not have a testimony of the Book of Mormon cannot be used as evidence that they have "failed to reach the conclusion" specified by Moroni, insofar as they have never had opportunity to read it and ask God for themselves:
For there are many yet on the earth among all sects, parties, and denominations, who are blinded by the subtle craftiness of men, whereby they lie in wait to deceive, and who are only kept from the truth because they know not where to find it— Therefore, that we should waste and wear out our lives in bringing to light all the hidden things of darkness, wherein we know them; and they are truly manifest from heaven— These should then be attended to with great earnestness. (Doctrine and Covenants 123:13-15)
