Harzer,
Your point is well taken with regard to [
have] and [
be]. You point out that these auxiliaries combine with verbs to form aspects. However, your analysis breaks down when it comes to consideration of [
do]. It is characteristic of aspect that it reveals the speaker's interpretation of the temporal elements of the event. It is clear that verb phrases formed with [
be] and the ‘-
ing’ form of a verb show the speaker as interpreting the event as “continuous”, that is, having a temporary duration.
She’s taking a test.
They’re eating lunch.
I’m writing a letter to my girlfriend.
Similarly, verb phrases formed with [
have] and the past participle form of a verb show the speaker as interpreting the event as “retrospective”, that is, looking back (in time) upon the event. This can be done from three different points-of-view, namely, from a point in present time, or a point in past time, or a point in future time.
He has gone home.
They had been there before.
Robert will have left before she gets there.
Your point about the auxiliary taking on markers in place of the verb is very interesting. I have not heard it explained that way before, and acknowledge that it seems to be true. That even seems to be the case with [
do], although [
do] does not mark aspect like the other auxiliaries you mentioned.
She does go to school every day.
They do work hard.
He did come home late last night.
These sentences do not show the speaker's
temporal interpretation of the events; hence the verb phrases in them are not marked for aspect. Perhaps this is what you meant when you said that “
go” in “
he does go” is no longer marked at all.

That’s quite correct. The verb form used is the basic, or infinitive form (without “to”). This form is also used whenever a
modal auxiliary is used in a verb phrase.
Sure, he can come over tomorrow.
Could you pass the salt please?
They will be home by now.
I might take a walk in the morning.
May I help you?
Modal auxiliaries, in addition, do not take on 'person' markers for verbs as do [
have] and [
be] and [
do] when they are used as auxiliaries. Since there are nine of them, and only three of the others, I guess I was thinking of the ‘typical’ case when I suggested they do not accept person markers. Thank you for pointing out my mistake.

Because, however, it is more 'typical' for auxiliaries not to take on characteristics of verbs, it is still my contention that we are better off calling them
auxiliaries rather than
auxiliary verbs!
Larry Latham