Indeed, that's the problem: the boxing process isn't unique—the ownership of the resultant box is.
Indeed. And I gave the same criticism of UniqueArray.
But it was decided then that we're now using Unique to mean "uniquely owned" as a term of art:
Indeed. But by making it a term-of-art, it is now true—it's a box and it's Unique, but still it's uniquely owned and not uniquely boxed.