(1) All of the examples you cite are noun compounds, i.e. combinations of two lexical roots that function as a single noun. The left element is always a modifier and the right element is always the head in such structures in English (unless we’re dealing with a headless compound).
(1a) [Noun [Root modifier] [Root head]]
(1b) [Noun [Root orange] [Root juice]]
(= Structure of English headed noun compounds, illustrated with "orange juice")
The term ‘compounding’ refers to a word-formation process in morphology; the term ‘complement’ refers to a structural relation with a head in syntax. The term ‘complement’ is therefore used in a confusing way in the cited section of the CGEL.
In terms of the internal structure of a noun compound, the left element should quite simply always be classified as a modifier and never as a complement.
One might try to classify the modifier element in noun compounds into a, let’s say, ‘typical modifier’ and into a ‘more complement-like modifier’. However, as far as I can see, there is no principled way to accomplish such a classification.
(2) How can we show that the left lexical root in noun compounds is always a modifier, and never a complement?
(a) Order. Normally complements (COMP) sound much better when they are close to their head while modifiers (MOD) can be further away from their head.
(2a) [NP a student [COMP of linguistics] [MOD in first year]]
(2b) ?* [NP a student [MOD in first year] [COMP of linguistics]]
(= Since “of linguistics” is a complement of “student”, it must be close to “student”. In contrast, “in first year” is a modifier on “student”, so it can be further away from “student”.)
There is no such (strong) ordering restriction on left elements in noun compounds. There are preferences and more plausible orders, but no fixed orders whose violations would lead to unacceptability. That shows that left elements of noun compounds are not complements.
(3a) a [Noun [linguistics] [first-year] [student]] (emphasis on “first-year”)
(3b) a [Noun [first-year] [linguistics] [student]] (emphasis on “linguistics”)
(= Both "linguistics"-"first year" and "first-year"-"linguistics" are permissible orders of the elements to the left of the head "student".)
(b) Number. There can typically only be one complement per (nominal) head but a large number of adjuncts.
(4a) ?* [NP a student [COMP of linguistics] [COMP of mathematics] [COMP of English]]
(4b) [NP a student [MOD in first year] [MOD in London] [MOD in college]]
(= The complement of “student” can only be realized as one “of”-phrase, but there can be many modifiers in the form of “in”-phrases)
Left elements in noun compounds can be added repeatedly independently of their meaning. The resulting compounds may be odd, semantically implausible or stylistically “ugly”, but they are not ungrammatical. This demonstrates that these left elements are not complements.
(5a) a linguistics-mathematics-English student
(5b) a first-year London college student
(=The left-elements in a compound headed by “student” can be numerous, irrespective of whether they denote subjects of study of the student or ancillary information about the student)
(c) Extraction. Normally you can extract out of complements, but not out of modifiers.
(6a) [NP a student of linguistics]
(6b) He loves linguistics, which he is [NP a student of _ ]
(= Since “of linguistics” is a complement of “student”, you can extract “linguistics” out of it.)
(7a) [NP a student in first year]
(7b) ?* He loves first year, which he is [NP a student in _ ]
(= Since “in first year” is a modifier on “student”, you cannot extract “first year” out of it.)
As it is impossible to extract out of the left element in noun compounds, these elements should not be classified as complements.
(8a) a [Noun [corpus linguistics] student]
(8b) * He loves linguistics, which he is a [Noun [corpus _ ] student]
( = If “corpus linguistics” was a complement of “student”, we should be able to extract “linguistics” out of it)
(9a) a [NP [post first-year] student]
(9b) * He loves first year, which he is a [NP [post _ ] student ]
( = Since “post first-year” is a modifier on “student”, you cannot extract “first year” out of it.)
(3) The only way to accomplish a categorization of the modifier element in noun compounds into, what one might call, ‘typical modifiers’ and ‘more complement-like modifiers’ is by reference to intuitions about their meaning. This is most likely what the CGEL authors had in mind. However, dependence on intuitions is unreliable and will run into problems with more complicated, fuzzy, atypical examples of noun compounds.
For complement-like modifiers, the meaning of the modifier is entailed by (or semantically obligatory for) the head. It involves information about central, important, crucial aspects of the head. In most cases, the relation between the compound head and its modifier corresponds to the relation between a verb phrase head and its complement. Also, the compound noun may have a of-paraphrase.
(10) a linguistics student
→ if you’re a student, you necessarily need to study something (entailment)
→ the subject of study is crucial to being a student (centrality)
→ “a linguistics student” ≈ “(to) study linguistics” (similarity with syntactic complement)
→ “a linguistics student” ≈ “a student of linguistics” (of-paraphrase)
CONCLUSION: As a left element of a noun compound, "linguistics" in "a linguistics student" is a modifier. However, it can be described as a complement-like modifier since it shares properties with complements in comparable syntactic structure.
For real modifiers, the meaning of the modifier is optional (or semantically uncompelled) with respect to the head; it involves information about non-central, unimportant, additional aspects of the head. In most cases, the head will not have a verbal analogue. A paraphrase with of will not be possible.
(11) a first-year student
→ if you’re a student, you don’t necessarily need to be in first year (no entailment)
→ the time when you started studying is not crucial to being a student (non-centrality)
→ “a first year student” ≠“*? (to) study first year” (no similarity with syntactic complement)
→ “a first-year student” ≠ “*a student of first year” (no of-paraphrase)
CONCLUSION: As a left element of a noun compound, "first year" in "a first-year student" is a modifier. Moreover, it is a typical modifier because it shows no similarities with a syntactic complement whatsoever.
(4) Regarding the other examples you mentioned:
(a) Since they are all noun compounds, they all involve left modifiers and right heads. The distinction between modifiers and complements is misleading in the area of word-formation.
(b) If you insist on making a distinction between typical modifiers and complement-like modifiers, then you could try to apply the semantic intuitions mentioned above: entailment, centrality, similarity with a syntactic complement and of-paraphases. You will then find that it is indeed often problematic to rely on semantic intuitions for linguistic classification.
(12) a college student
→ if you’re a student, do you necessarily need to be anywhere –no (no entailment)
→ the place where you study does not seem crucial to being a student (non-centrality)
→ “a college student” ≠“*? (to) study college” (no similarity with syntactic complement)
→ “a college student” ≠ “*a student of college” (no of-paraphrase)
CONCLUSION: (a) As a left element in a noun compound, college is a modifier.
(b) It may also be a fairly typical modifier based on semantic considerations.
(13) a police station
→ if there is a station, does it need to be for someone or contain something – probably not (probably no entailment)
→ the benefactive of the station does not seem crucial to me (non-centrality)
→ there is a parallel between “a police station” and “to station police” but the meanings may be somewhat different (some similarity with syntactic complement)
→ “a police station” ≠ “?* a station of (the) police” (no (normal) of-paraphrase)
CONCLUSION: (a) As a left element in a noun compound, police is a modifier.
(b) It may also be a fairly typical modifier in terms of its semantics, but the fact that we can say to station police shows that in the domain of syntax, a similar construction would allow police to function as a complement of station.
(14) a tax bill
→ if there is a bill, does it need to be about something – I think so, yes (entailment)
→ is the content of a bill crucial to the concept of “bill” – maybe (maybe centrality)
→ there is a parallel between “a tax bill” and “to bill tax(es)” but the meanings of the latter is very strange (almost no similarity with syntactic complement)
→ “a tax bill” ≠ “??? a bill of tax(es)” (very odd of-paraphrase)
CONCLUSION: (a) As a left element in a noun compound, tax is a modifier.
(b) It may be a more complement-like modifier from the viewpoint of its meaning because the concept of a legal bill entails that there must be some content of the bill – a bill must be about something, such as taxes.