The Concise Oxford Dictionary lists nine uses of which the possessive is but one. The use of the objective relation is seen in "love of virtue," "search of knowledge," and applies to "faith of Christ."
Of course "of" can have ambiguity
in other contexts in the presence of other words. That much is obvious, and is a fact I have not denied or contradicted even for a moment. However, we all know that, in English, "of" does not function in any possible way at any given moment. That is a fallacy akin to an illegitimate totality transfer, and thus citing there merely plethora of
possible meanings does not really help your argument. In fact, it actually doesn't really say anything other than the fact that "of" can simply function in a great number of ways
in a great number of contexts; but this is true of many, if not all, prepositions.
In reality, "of" functions differently in the presence of different types of words (i.e., in different contexts). For example, how does the preposition function when the object is personal? One of the problems with the examples you gave (in your original comment, which you edited, and which I quoted above) is that none of them you gave have a person as the object of "of." Virtue, being impersonal, cannot possess love, so the fact that "love of virtue" is an objective genitive is more because of the impossibility of possession than because of the preposition. However, when the object of "of" is a
person, we begin to have a problem, because a person, unlike a concept (e.g., "virtue") is capable of both possession and exercise of a verbal noun. Thus, ambiguity is introduced, not necessarily because of the nature of the preposition, but the possibilities introduced by the situation introduced by the functioning of the concepts communicated
by all the words in context.
Another question is this: How does the function of the preposition change with the presence of different verbal nouns? In English, there is indeed ambiguity, for example, in the phrase "love of God": it could be objective ("love for God") or subjective ("God's love"). Again, this is because the object of "of" is personal, as opposed to impersonal. Just like in Greek, certain English verbs and verbal nouns take on different meanings in the presence of different prepositions. "Faith" is one of these verbal nouns. I have never heard anyone say, when they want to communicate, for example, their objective faith in the sturdiness of the chair in which they sitting, say, "I have faith of this chair." Such a statement is non-English, and communicates only that the speaker does not have total command of the English language. Rather, to communicate their objective faith, they would say, "I have faith
in this chair." The reasonable conclusion: "Faith
in" and "faith
of" communicate different things in English. I would dare to assert that I highly doubt if even a single English speaker, being presented with the phrase "faith of Jesus Christ," would interpret it in
any other way than possessive. It just simply is not how English functions in this scenario, given these particular words joined together by this particular preposition.
That is why "word-for-word," while it is perfectly fine most of the time, is not acceptable in some instances. This is because words are not
merely (notice my very deliberate word choice) symbols packed with meaning. Rather, they are symbols packed with meaning strung together to
function a certain way. The vast majority of the time, the function of words strung together in one language maintains well when translated into another language; this is when "word-for-word" works well (which is, again, most of the time). However, this is not always the case. Many times, the
function (without which there is no meaning) cannot be maintained through a "word-for-word" rendering. It is my argument that πίστεως Ἰησοῦ Χριστοῦ in Romans 3:22 is one of these occasions. Not only this, but it is a particularly difficult situation because of the fact that the limitations of English force translators to make a choice.