I think the best answer has already been stated in a previous post. LDS use the KJV because it was the bible in use at the time of Joseph Smith. It doesn’t have anything to do with accuracy. There are more accurate English translations today than the KJV. I don’t think that is in great dispute among scholars. The BoM was written in the same form of English as the KJV, so if the LDS were to accept a modern English translation of the bible, they would also have to translate the BoM, D&C, and Pearl of Great Price into modern English as well. I don’t think they want to do that.
This whole debate is somewhat silly because it only deals with English. Another poster has been complaining incessantly about modern translations. But the truth is that it’s no different translating into modern English than it is into other completely different languages. The bible has been translated into almost every language on earth. Does KJV English mean anything to Japanese, Chinese, French, Italians or someone from an African country? No, of course not. The bible is translated into those languages as well. There is never a perfect translation from one version of English to another, let alone into completely different languages. But somehow the bible has been miraculously preserved through all these translations.
The bottom line is that scripture must be translated into languages currently spoken by all peoples in order for it to be understood. That includes English, and as the English language has evolved new translations must be made in order to preserve, not change, the original meaning of the authors. This is done through painstakingly difficult scholarly work. I thank God for them and I believe that the Holy Spirit has guided them throughout the centuries to preserve the bible.
Now scripture is not the final arbiter of what scripture means. When man takes that approach, new denominations are created. There must be an official interpreter. The Church existed before the bible as we know it today. It is the Church, not scripture, that is the “pillar and foundation of truth” (1 Tim 3:15). The Catholic Church is the only church that has been doing this for 2000 years. That is where I place my trust. I refuse to fall for the conspiracy theories of Mormonism, Jehovas Witnesses, Seventh Day Adventists, and many others who attempt to tear down the original Church of Christ in order to legitimize their own existence.