> CGEL says this

On further investigation I guess that Old English did indeed have a dedicated subjective conjugation, unique at least in the plural!

> good luck identifying why a verb appears in the subjunctive if you can't see the rest of the sentence around it.

The question of _why_ a verb is in a particular conjunction is one thing; the question of _whether_ a verb is conjugated, though, shouldn't really be in doubt.

> A verb form is never sufficient to signify the semantic mode of a sentence.

In languages with conjugated grammatical mood, the conjugation is indeed enough to signify the mood of the verb, just as in languages with conjugated past tense verbs in the past tense can be recognized by their conjugation.

> So, for English, we have a distinction in semantic modality that obligates us to use an exotically-conjugated verb. Why is this not an example of grammatical mood?

I think we might be talking at cross purposes. English certainly does have (several! though the precise set might depend on whom you ask) grammatical moods (in the English-grammar sense of grammatical constructions that convey mode). I don't know of anybody who argues that it doesn't. What English doesn't have, and Turkish (as well as Latin) does, is _conjugated_ mood, i.e. a particular mutation of verbs that associates a particular mode with that verb.