Ultimately, I believe you’re correct.
For now though, “Morale Officer” sounds so much more inviting and “inclusive”.
Truthfully though, during DS/DS, our Chaplains were called Morale Officers because we weren’t supposed to be open about non-islamist services.
I use the term quite loosely here as our military is not what it was 20+ years ago.
Under this regime, the primary duty of a C.O. is to be a commissar to control the thoughts of those in your command. We will be screwed when a real shooting war happens and all the get is sensitivity training