Simple present in the form of a statement in English also doesn’t have auxiliary verbs, they appear when you negate something or ask a question.
Auxiliary verbs would be like:
делать я хочу поговорить? (Do I want to talk?)
or
я не-делать хочу поговорить. (I don’t want to talk)
which isn’t the case in Russian.
When speaking about future, we may or may not use the word “буду”. For example, you can choose to replace
я буду говорить (I will speak)
by this
я поговорю (I will speak)
Your examples are more like the modal verbs, they describe your relationship with the action you’re going to perform.
It’s mostly semantics. I agree that the blunt notion that “there are no auxiliaries in Russian” without any context is questionable at best and misleading at worst, so you make a good point there.
However, not every verb that can combine with others is an auxiliary. What exactly counts as such is a fuzzy issue but the main point is that sometimes verbs can serve just to provide information about other verbs (mostly conjugation) without contributing any meaning of there own. Those would be “auxiliary”. The prototypical examples is “have” in sentences such as:
Here “have” doesn’t mean “possess, own” as in its proper sense but serves only to modify “see”.
In your examples:
Должен is not even a verb, so it doesn’t count
Собираться has a clear meaning of its own; if you consider any verb that can combine with others as auxiliary, then “appreciate”, “plan”, “suggest”, “command” and many, many others would be “auxiliary”, because you can say “I appreciate your coming”, “I command you to clean up”, “I plan to go fishing”, … Btw, the last example shows that even “go” can combine with another verb.
Мочь is a borderline case. As S.I. pointed out, it’s a modal verb. Are modal verbs auxiliary? It depends on who you ask. In English, modal verbs (can, must, …) are sometimes considered auxiliary, sometimes not. The equivalent Spanish verbs (poder, deber, …) are clearly not considered auxiliary: the reasoning is that they do not provide conjugation information but a meaning of possibility, will, obligation, …
Я буду говорить: I see a very strong case for considering буду in this case as an auxiliary, so I do agree with you. It’s hard to see why the definition would not apply: it only serves to build up a future tense.
So, thank you for the “philosophical” discussion. It’s interesting to discuss these points. From a practical standpoint, however, the “there are no auxiliaries in Russian” slogan is simply not a useful remark.
Thanks for your input. I don’t have a clear understanding of grammar other than “tribal knowledge” of English. I vaguely recall “past perfect, future tense, past continuous” and what not from decades back but I don’t have the meaning clearly burned in. When I was learning Spanish I just mapped constructions directly from English to Spanish and I took more or less the same approach with French. I was indeed thinking of poder, tener, deber etc.
With Russian I’m now at the stage where I need to build a repertoire of valid constructions or else I’m going to be stuck with pidgin-Russian so this is why I’m mulling stuff over.