They are actively fulfilling a Biblical prophecy ONLY by determining genealogical lineage AND then baptizing the dead.
Simply baptizing them just makes them Mormon. In the minds of the LDS followers.
No, no, no, no, no.
Jesus Christ taught that baptism is essential to the salvation of all who have lived on earth (see John3:5). Many people, however, have died without being baptized. Others were baptized without proper authority. Because God is merciful, He has prepared a way for all people to receive the blessings of baptism. By performing proxy baptisms in behalf of those who have died, Church members offer these blessings to deceased ancestors. These individuals in the next life can then choose to accept or decline what has been done in their behalf.
You're missing a very, very key element here. Nobody is making anybody else Mormon. That would violate agency. Baptism is a covenant, like a contract. It is a two sided promise. It is valid if, and only if the deceased accepts it. Thus, they are NOT recorded as becoming Mormon, but as having had the saving ordinances performed on their behalf. It is up to them to decide whether the ordinance is valid or not.
This misunderstanding has lead to a lot of unnecessary anger (and heated rhetoric) over the years. Please don't perpetuate it.
Further, it is widely accepted that there will be a thousand years of peace, called the millennium after the return of Christ during which angelic messengers will facilitate cleaning up records that are inaccurate, or no longer exist on behalf of those who still want ordinances performed. The reason to not wait stems from the desire not to make those who are eagerly awaiting the work wait any longer.
For more information on the motivation for Temple proxy work, see:D&C 137. (Note that the Biblical term "prison" is understood as a spiritual state regarding sin, and not a literal one, that baptism facilitates freedom from.)