Mormons give all kinds of reasons for not using the Cross as a visual symbol. Some of them were just made up by someone trying to think of a reason for the practice, while others have been given by Church leaders. Gordon Hinckley once said that we don’t use the Cross because we prefer to dwell on Jesus’ triumph over death, rather than his death, in our symbology, for instance.
But the problem isn’t that we don’t acknowledge a central role to Christ’s crucifixion. “And so it was made known among the dead, both small and great, the unrighteous as well as the faithful, that redemption had been wrought through the sacrifice of the Son of God upon the cross” (D&C 138:35).
In any case, I think many of these explanations, including Hinckley’s, are fine, but they sort of politely dodge what I see as the core issue. Lots of Christians have not just used the Cross as a symbol, but have venerated it in a way that smacks of idolatry to us. “Thou shalt not make unto thee any graven image, or any likeness
of any thing that
is in heaven above, or that
is in the earth beneath, or that
is in the water under the earth: Thou shalt not bow down thyself to them, nor serve them” (Exodus 20:4-5). The Israelites didn’t interpret this to mean that they couldn’t use ANY statues or symbols, and that sort of thing. They had some in the Temple. But they didn’t bow down to those images. Contrast that with your typical Catholic entering a church and genuflecting to the Crucifix.
I know, I know–Catholics don’t see this as “worshiping” an image. I’m glad of that. But the commandment clearly says not to “bow down” to any likeness of anything. I understand that you guys don’t buy that argument, but I’m just trying to explain why I don’t think we use the Cross.
That is, you ruined if for us.

JWs like to point out lots of Christian symbols (like Christmas trees and Easter bunnies) that are Christianized pagan symbols, but Mormons are usually fine with all that. Christmas would suck without Santa and all the rest, if you ask most of us. But I think we react differently to “paganized Christian symbols” like the Cross. So many hundreds of millions of people are used to genuflecting to Crucifixes, that it’s probably best to just tell them to lose the Crucifixes if they join us. Otherwise, I think there would be crosses all over Mormon buildings.