An Elf with shapeshifting ability? Why?

[obloquy]

Originally Posted by Elemmakil

IIRC correctly, Luthien's ability to shift shape does indeed come from her Maian ancestry. This was ability shared by all the Ainur, and examples of it abound. Note Sauron's ability to take the form of a werewolf and Olorin's practice of walking among Elves and Men unseen or in shape like one of them during the First Age. Luthien, as noted by another poster, probably would not have all of Melian's powers, but she would certainly would be expected to have powers beyond those of any other Children of Iluvatar.

No. The Ainur could change shape because in those instances you cite, they were not truly incarnate: they were ealar in physical "raiment." Luthien, on the other hand, was born, and therefore was fully incarnate from the start. Shapechanging among the Ainur was not a magical ability, it was their nature, as all forms were temporary for them; they had no natural physical shape. At least, not until they became incarnate--as Sauron, Morgoth, the Istari, and Melian did--at which point they lost the ability to change their physical appearance.