So, I suppose a good way to start this topic is why members of the The Church of Jesus Christ of Latter-day Saints hold such importance for missionary work. There are a few reasons that I can say just off the top of my head.
First, the Lord has asked that we share the Gospel with all so that they may have a chance to know of its truths and have the chance/opportunity to choose whether they want to believe those truths or not. It is actually a commandment. One given to us by the Savior Himself when He was here on Earth.
Matthew 28: 19-20
Related to that, while yes the Savior commanded us to share the Gospel, He also gave us another way that we can show our love for Him.
John 21: 15-17