I don't really get your question. "Why are some word classes not immediately dominated by a phrasal category" - any word is dominated by some phrasal category. Your question is probably rather about why some words are dominated by a phrase that doesn't have the same category as this word (e.g. D is not dominated by DP).
A node is always immediately dominated by the category that the head of this phrase determines. So the nodes in an NP will be dominated by NP because the head of the NP is an N, the nodes in a VP will be dominated by VP because the head of the VP is a V, ...
It seems like in this syntax theory, NPs can also contain (optional) determiners, but whatever else there may be, whether there is also a D, a PP, ..., the head of the phrase is still N, and this is what determines the category of the NP.
I haven't read that book myself; either there is also the notion of DPs that is not shown here or (more probably) all DPs are considered NPs - this is an eternal dispute among syntax theories, some argue that it is more reasonable to assume D is the head of a phrase like "the cat" because, amongst others, the choice of the determiner influences the inflection of the N so one can assume that NP is more like a complement to D that gets selected by it and so on, some prefer to go with the more traditional assumption that the head of such a phrase is still an N and that determiners are additional (if you stick to the assumption that all NPs must eventually go into DPs, you must assume an empty determiner head in a phrase like "I like [ø cats]") so the phrasal category is an NP.
You say "for example, per (d) ...". What else do you mean? I don't see anything more that looks weird.