On its own. But it works just fine for initiating a process of elimination, as I did.Whilst possible, this amounts to employing an absence of evidence as evidence of absence, and is thus never going to be logically compelling...
Only Iluvatar could create spirits or souls, and gift them with free will. Any Ainur could create (false, or soulless) life, and from that bodies; otherwise, dwarves and ents would never have been come into being (Aule having created the dwarves, and Yavanna having asked Iluvatar to gift her trees with souls), and Maiar could not incorporate. Creating a physical body into which Melkor bound an umaiar would have been entirely within his power.
Diminishing himself by suffusing his servants with his own power is exactly what Melkor did do. To the point he was so diminished by the War of Wrath he was defeated and captured by an elf-lord and an eagle. It's the precise mechanism by which Melkor was bound to Arda itself, despite being bound and cast to the Void his power lingered; Arda is "Morgoth's ring".