Nevertheless the case of Witch-King of Angmar is very intriguing, if the Nazgul were merely some extensions then he doesn't really get much credit for destroying Arnor.
Exactly, it's hard to imagine someone as powerful as the Witch - King as just an extension of Sauron, even though it is partially true. But he must've had some power of his own too, as we're told the Nine were great kings of men, not some randoms.