As a rule we would drop the article in a prepositional phrase when the noun was plural or a countless sense:
They watched with gazes of horror
Cooked in milk.
It was though once more common to drop the article when the preposition was used to supply a state that applies to the previous clause:
That slepen al the nyght with open eye [Chaucer, "General Prologue", Canterbury Tales]
This is the use that both Wilde and Poe used. However, both of these poets would sometimes use language that was old-fashioned even for their day, so as well as fitting the meter, the unusual usage adds a degree of emphasis.
It's not a use that one should normally use today.
Tradition
The term "article" is relatively old, and grammatical terminology has a certain amount of inertia. So this is partly a historical question: why did the word "article" come to be used to refer to some words, but not others in English? Unfortunately, I don't know the answer to that historical question, so I'll try to provide alternative explanations (although I think without historical background this is necessarily an incomplete answer).
Frequency
Words that are called "articles" are generally among the most frequently used words in a language. "The" definitely qualifies, being according to a variety of online sources the most frequently used English word (e.g. Wikipedia). "A" also seems to be in the single digits ("an" is lower, but if we consider it to be the same word as "a", just an automatic phonologically conditioned variant, this doesn't really matter), with only other common function words like "and" outranking it.
"Any" seems to rank around 100 or so. This is certainly very frequent, but in most of the lists I found that means it is less frequent than at least a few common content words such as "one" or "know".
At least some syntactic theories may distinguish articles from (at least some) other determiners...
I am not a syntax expert so I can't really say how articles might form a syntactic class relative to other determiners, but apparently some people think they do.
I found "The Internal Syntax of Determiners", by Thomas Leu, a dissertation that presents his analysis of determiners in Germanic languages. It's too technical for me to understand most of it (well actually, I haven't even tried to read through it) but I did skim it and he does seem to analyze articles as structurally distinct from other determiners.
Leu says on page 1 that
This thesis is a comparative study of determiners (mostly) in Germanic, with an emphasis on Swiss German. A distinction is made between determiners (e.g. that, both, which, such, my, no) and articles (the definite marker and the indefinite article). Such a distinction has previously been argued for (see Szabolcsi (1994); Giusti (1997); Matthewson (2001)) and will in the present work be taken to syntactically be one between phrasal constituents (determiners) and heads (the articles).
One of the main claims he argues for is that
All determiners (other than the articles) consist of an extended adjectival projection, xAP (for the most part) (p. 2)
I did find and read the paper by Lisa Matthewson (2001) that Leu references, "Quantification and the nature of crosslinguistic variation". Matthewson brings up a point that I did not think of, that there is a distinction between the behavior of certain determiners, such as the definite article "the" or the demonstrative "these", and quantifiers such as "many" and "most" (which are also traditionally classified as determiners). The quantifiers can be used in what is called "partitive constructions" such as "many of the people" or "most of the people"; but we cannot say *"the of the people" or *"these of the people" (164). She argues from this and other facts (including comparison with other languages such as St’át’imcets/Lillooet Salish and French) that maybe English quantifiers don't take noun phrases as arguments, as determiners do, but rather take determiner phrases as arguments (although this might just be default behavior rather than a hard constraint). She doesn't explain "any" (in fact, she notes that a reviewer pointed out free-choice any as a "potentially problematic item" because it "can take a bare singular noun as its argument") but I found it an interesting read.
Giusti 1997 seems to be up on academia.edu (http://www.academia.edu/1032147/The_categorial_status_of_determiners._The_New_Comparative_Syntax_ed._by_Liliane_Haegeman); I haven't read it but I did look through it and she describes some criteria for calling a word an article.
But syntactic theory and terminology can be fairly diverse
Certainly, just because Leu writes this in his dissertation doesn't mean all linguists agree with it. I don't know how many linguists would agree that English articles are definitely distinct from the other determiners.
It's certainly not obvious, as you note, and I found some related posts that are dismissive of the meaningfulness of the term "article" in syntax:
one on Linguistics SE, Aaron's answer to the question Do some languages have articles besides the definite and indefinite articles?:
It is worth noting, I think, that "article" is not a theoretical primitive in (most if not all) contemporary generative theories of syntax. [...] articles are a notion of classical grammar and are definitionally restricted to the definite and indefinite."
two on Quora, Chrissy Cuskley's and Matthew McVeagh's answers to Asides from "the" and "a", are there any other articles that foreign languages use besides the 'usual' definite and indefinite ones used by the English language?:
in formal linguistics (though I think not so much in ESL/ language teaching generally), the category "article" is not much of a functional category. In my training in syntax we instead referred to determiners, of which the indefinite and definite article are only two types
(Chrissy Cuskley)
I agree with Chrissy that the term/concept of ‘articles’ is from traditional grammar, and was perhaps created to name those words which didn’t exist in Latin but came into existence in the Romance languages (along with Celtic, Germanic, Greek and Semitic). It is still used in traditional grammar and in language-learning, but not so much in scientific linguistics as it doesn’t really name a natural category. Instead what we call ‘articles’ are just a subset of ‘determiners’, a category created by linguistics based on actual evidence of a common syntactic role.
(Matthew McVeagh)
Your numbered points
1, 2): as I said, many people would consider "a" and "an" to be two forms of the same word, rather than two distinct words. But this isn't super important.
3) “Any” really doesn’t function like a plural equivalant to “a/an”, so this part of your argument is not convincing to me. As you note, they actually contrast before singular nouns. “Some” is certainly a better candidate for a plural indefinite article in English in my opinion (although it also has the problem of contrasting with "a/an" before singular count nouns).
5) Sure, in the mainstream analysis a plural indefinite article doesn’t exist in English. You should explain why this is a problem; it’s not obvious that it is.
In fact, I know of a (minor) piece of evidence that there is no plural indefinite article in English: the so-called “Big Mess Construction”, which is the use of an adjective before an indefinite article in some contexts such as “not that good a book,” “not so serious a problem” (I talked about this more in another post: If I can say “not that good a review,” does that mean I can say “not that good reviews”?). This construction does not work with either “any” or “some”: *“not that good any books”, *“not that good some books”.
I can't think of any good reason why an indefinite article being plural would disqualify it from being used in this construction. A more satisfying explanation in my opinion is that "any" and "some" don’t work here because they differ from "a/an" not only in plurality, but also in part of speech: that they aren’t indefinite articles, and the “Big Mess” construction requires an article, not just any kind of determiner.
Best Answer
This is the classical expression. The term was used by the Catholic Church (from 1587 until the office was abolished, in 1983) for the canon lawyer who was supposed to argue against proposals for canonisation, i.e. adding someone to the official list of saints, the canon. The purpose of these arguments against canonisation was to test the strength of the arguments for canonisation as brought forward by God's Advocate.
Syntactically, it is ambiguous whether the modifies Devil or advocate; however, in this case it must modify Devil. That is because the Devil normally requires the definite article if you are referring to the one and only Christian Devil, which is the case here. The definite article can sometimes be left out, but that would be ellipsis; in that case, however, advocate shouldn't have an article either, because Devil requires it while advocate doesn't. Compare the following sentence:
Being someone's x usually doesn't require an article before x. Whose advocate is he? The Devil's! It would be odd to add the article where it is normally left out (with advocate) while omitting it where it is normally used (in the Devil).
The indefinite article sounds less idiomatic. The article the as above could be left out in casual use; but then it would sound odd to use a phrase almost identical to the full classical expression the Devil's advocate, having merely swapped one article for the other. If you mean to say that a specific person answers to this description, use the; if you were mentioning the general concept of being a devil's advocate, you could very well use a.
Here the article is dropped in a casual manner, and the phrase is used loosely in a slightly changed environment: this is how the phrase is most often used.