While I'm not quite sure when the whole "closed species" trend started or who started it (even better question- "or why"), I did a little research on if it's actually possible to copyright a fictional species.
The short annswer? No.
But why? Keep reading.
Though many people believe that copyright protects a creative work no matter what the form- this is not the case; if it was, there would be no patents or trademarks. In fact, there are several categories of creative works which copyright does not protect. One such category is ideas. Since a closed species does not take a specific form, it can not be copyrighted. These closed species are only a set of common attributes as ideas which make it identifiable- that means it could be covered under a trademark as it would identify the artist or their services, but not a copyright as it is only an idea and intangible on its own and members of the species have their own unique attributes (thus making a derivative work) which would technically differentiate them from the original definition of the species. Also, a copyright is only applicible to tangible works, making it even more impossible to gain a copyright over a fictional species as the fundamental components of the species are intangible and ideas- neither can be copyrighted.
Please note I am not a lawyer and just a fur with some knowledge about this stuff, but I did choose reliable sources of information.
Sources: LegalZoom and the United States Patent and Trademark Office