This is a more significant, and disturbing, reason that the LDS Church shuns the symbol.
Again, it is generally accepted by all Christians that the cross was, and is, a symbol of torture. And yet the real meaning of that Crucifixion makes the cross an extremely appropriate symbol for anyone who professes to be Christian.
The LDS Church focuses on the living Christ, which is good, but taking the "no cross" stance could imply that Christians who acknowledge the significance of the cross and its association with death, underestimate the significance of Christ's resurrection. The Crucifixion and resurrection of Jesus are part of the same story.
The New Testament describes very clearly the events leading up to the Crucifixion, the Crucifixion itself, the aftermath, and the resurrection. Without one part, the other parts are incomplete. Fractional Christians cannot be effective.