Q. Why do members dress the deceased and not the funeral directors?
In many cases members of the Church dress their relatives for the grave rather than having the funeral directors do so. To understand why, some knowledge of the LDS temple ceremony is essential. One purpose of the temple is to prepare a person to meet God in the afterlife, part of the process includes the wearing of certain ceremonial clothing which has significance to those who go through the temple. So when Mormons die, if they have been through the temple and received the ordinances then they can wear the ceremonial clothing in preparation for their day of resurrection.
If a funeral director were not a member of the church he would not understand the clothing nor the significance it holds for members. Therefore when members of the church die family members or ward leaders take on the responsibility of dressing the body.