Full names are not necessarily unique either.
Indeed. A few years ago, I ran across a US Census Bureau web page that gave the number of people with specific first or last names, and an estimate (likely from multiplying the fractions) of the number of people in the US with a given first+last name. It said that there are about 1800 people in the US with the same name as me, and my family name isn't even Smith or Jones or any of the other top 100.
Through the years, I've seen a number of bibliographies that list things that I've written, intermixed with things written by various of those others with my name. So far, I haven't complained, since this makes us all look better than we really are. ;-)
Still, it could be useful if we had a reasonable way to separate out such things and give individuals the proper acknowledgement for their contributions to our knowledge. But I'd be surprised if we could actually do this job right, within the lifetimes of people now living.
Among those of us familiar with the old music of the British Isles, one ongoing frustration is the misattribution of music written by Niel Gow or Neil Gow. One of those was the grandfather of the other; do you know which was which? The intermediate in the male line was Nathaniel Gow, who also wrote a lot of good tunes, and collectors also confuse him with his father and his son despite the different name. Somehow, I suspect that this Unique ID system won't be extended to them, any more than I expect it to be implemented accurately for living authors.
(And none of this will stop current publishers from claiming copyright for their works. ;-)