Once again, piece by piece...
Oxford defines an auxiliary verb as
- a verb used in forming the tenses, moods, and voices of other verbs
This definition is not restricted to English. English does, however, have its own
collection of prominent auxiliary verbs; the most common are
and the modal auxiliaries
- must, may, might, can, could, shall, should, will, would, and sometimes need and dare.
Note that all of these English auxiliary verbs are in fact verbs. Single verbs. No prepositions, articles, particles, quantifiers, or adverbs -- no extra words attached; just the verbs. That's what Oxford is saying.
However, going to is never listed as one.
However, be going to has stuff attached. It's not a verb so much as an idiomatic construction like there is. Some form of be is required before the progressive form going (and it has to be the progressive form only), and then to has to come right after going.
So it's not an auxiliary verb. What it is is a paraphrase of a modal, in this case the modal will, often used to indicate the future like most modals. That's not the future tense (there isn't a future tense in English), but it is a modal meaning, so in fact it's like an auxiliary verb, though it's made and used differently. The technical name for it is a periphrastic modal construction.
There are a lot of them. Most modals have one or two. Since modals can't take tense and don't have infinitives or participles, they can't be used in a lot of ways, so we use the periphrastic modal constructions instead:
- *Yesterday I musted skip breakfast. ~ Yesterday I had to skip breakfast.
- *He must have been willing leave ~ He must have been going to leave.
Have to paraphrases must, be going to is will, and ought to (without auxiliary be) is should. Each is idiomatic and has its own usages and idioms.
It would seem fair to consider it such since it is a common way to construct the future in English.
All modals and modal paraphrases are common ways of constructing a future meaning. That's not the future tense, however; that's just imagination.
- Bill will/must/has to/may/would/intends to/is going to leave tomorrow.
All of the variants above refer to the future; are they all future tense?
Of course not; there is no future tense in English.
Would it be wrong to consider it an auxiliary verb?
No, not as long as you can consider the quick brown fox to be a noun; a periphrastic modal construction is a phrase being used as an auxiliary verb, just like a noun phrase is a phrase being used as a noun. This is the principle of constituency -- words can aggregate into phrases with the same use. And when that happens with grammatical parts like auxiliaries, the new constructions get very very idiomatic and irregular because they're frozen in place.
If so, what is the reasoning behind it?
It's not, so don't worry about it.
Summary: Don't depend on dictionaries for grammatical information. That's not what they're for.