I think your post shows the reason for the change. The church is Christian in that we believe in and worship God through Jesus Christ as our savior. Many people don’t view members of the Church of Jesus Christ of LDS as Christian. They take the name Mormon and think we worship Mormon, or something like that. I don’t have an issue of making sure we keep Christ in the name of the church as we make reference to it, even understanding it can be inconvenient.
Maybe the issue is in the definition of what people view Christian as. It seems as if Christian is used to define a branch of Christianity, as Pentecostals and Calvinists are still Christian, correct?
Why would a member of this church be any different if we also believe in and worship Christ?
The term Mormon did start out from enemies of the Church of Jesus Christ of Latter Day Saints. It did turn into something that was accepted as a descriptor and something easier to say than the long name of the church. I get that the origin of the term was not positive, but saying that I don’t think that should be the main reason to move away from it. The term Christian started out also as a derogatory term used by non Christian people to refer to followers of Christ.
My take away is that the change is being used to clear up confusion of other Christians as well as just other people in understanding who the members of the Church worship, and who is most important in our beliefs. It is not Mormon, or any of the other Book of Mormon prophets. While they are important, they are only important as they point the way to Christ.
The secondary and tertiary reasons for the change are just that, smaller less important reasons to do this that may have flawed foundations on their own.