While
davendë 
, as always, makes a very persuasive argument, I think it might be interesting to step back for a bit and ask why there is this sense that other Middle-earth stories could be written.
Obviously, there are holders of copyright who have sold the right or have hired other writers to pen stories of their universe. Top names here are Gene Roddenberry of Star Trek fame and George Lucas of Star Wars fame. Interestingly, both of these universes became known to fans first visually through the drama of film or television, rather than in written format. Both those media employ stables of writers; screenplays and TV scripts are cobbled out of a group effort. Royalties accrue to the original creator (or his estate, in the case of Roddenberry), but no one would ever say that others cannot participate in the concept. Who can is controlled by the business enterprise.
Now, Tolkien didn't come to us this way initially. He came in book form, and his books are substantively different from the early writings of the Star Trek and Star Wars universes. But two things have happened to Tolkien since his initial publication: Peter Jackson's film and Christopher Tolkien's productions.
The presence of the films, with their legal right to use the name Tolkien, makes it difficult for many people to distinguish between Tolkien and these Hollywood fantasists--rightly or wrongly. People are going to ask, why not with T as with R and L? The fine points of arguments about canon make little sense given that the practice is so widespread. (Note, I'm not agreeing with this; simply pointing out that many people will want to know why this is an apples and oranges argument when what they expect is the ambrosia of mixed fruit.)
The role of Tolkien's literary executor has substantially muddied this situation. What are the specific instructions Tolkien left for CT? True, literary executors do generally have the right to bring to the public eye postumous works of writers. Yet how many literary executors have done what CT has done--pulled together books from separate pieces of writing. The guiding principle here has, I think, been CT's understanding of the Legendarium and his desire to bring narrative continuity to the fragments which his father left. The son clearly had "access" to his father's understanding of Middle-earth and a sincere and profound imaginative grasp of it and of many of the works which went into his father's cauldron of stories. Clearly, no one will ever be in the same position as CT, who was offerred drafts of LotR for commentary while the book was being written and who was the first audience for TH. Yet the very presence of Christopher Tolkien's work, compounded with the progessive and framentary nature of JRR Tolkien's writing habits, provides a context which creates this sense that a hard and fast canon does not close off the possibility of other stories.
There is a world of difference between CT the scholar and the writers of the ST and SW universes. Yet hasn't CT invited, even inflamed, the desire, whetted by these other situations, for other Middle earth stories? Once JRRT opened up his imagination to CT, a subtle knife cut into the canonicity issue and the dust spills over.