How foundational do you want to go with the why it works?
From my perspective, Rosenberg is a little superficial in many of his explanations about why things work. He doesn’t explore the evolutionary roots of behaviour and the general classes of behavioural strategies that seem to me to be foundational to why his methodology works as it does.
Particularly his explanations on pages 22 and 23 of NVC look only to relatively recent social forms, rather than looking deeper to the evolutionary and logic necessity of the rising of those forms.
When one looks from an evolutionary perspective, the picture is quite different, as we see patterns of development repeated in individuals, and changing frequencies of different modes of behaviour across populations and times, as a result of those individual developments.
And for the most part what he says works very well, and many of his explanations are adequate for most people.