Should other writers be able to use Tolkien's mythos for their own works?

This is what Tolkien, himself, had to say on the matter: "Once upon a time I had a mind to make a body of more or less connected legend, ranging from the large and cosmogonic to the level of romantic fairy-story - the larger founded on the lesser in contact with the earth, the lesser drawing splendour from the vast backcloths... I would draw some of the great tales in fullness, and leave many only placed in the scheme, and sketched. The cycles should be linked to a majestic whole, and yet leave scope for other minds and hands, wielding paint and music and drama." - J.R.R. Tolkien