As you request, let's assume the cognitive functions exist, they are meaningful, real, validated, everything we want in a psych theory.
Hypothetical example: some guy walks into a room at a party and is sizing up the situation, talking and joking with people, grabs a few drinks, etc. Fill in the blanks of this scenario as you prefer... and let's say you theorize he is using one of the extroverted perceiving functions either in the dominant or auxillary position. You can't really tell which just yet and not sure of the other functions....
But you're sure he has extraverted perceiving in the top 2.
The question is how do you determine whether his Se or Ne (whichever you decide) is his primary or secondary function? as stated earlier, Jung says that its not the function we are most adept at, its which is most often used, right? So he could have a strong/weak Fi/Ti or whatever in support of the extroverted perceiving, but that doesn't help you determine what's dom/auxillary.....
The ONLY way in this scenario is to tell whether his Se/Ne is occurring in the dominant or auxillary position is to determine whether he is an introvert or extrovert. But you wont be using the cognitive functions themselves directly to determine where they belonged as dom/aux, you have to resort to using one of the 4 XXXX dichotomies to narrow down where his cognitive function preference resides.
So the question is still kind of the same: Why bother pondering the person's cognitive functions themselves when you still have to base them on the XXXX letter type in order to determine whether its an dominant or auxillary placement? As you state in the OP, the aux is possibly as strong if not stronger than the dominant, so why don't you just try to sniff out the Guy's 4 dichotomies? Is he an extrovert ? is he F or T?
I'm not sure how clear I am being with this example, ill try to edit/clean it up a bit, but even if the cognitive processes are true and valid i still maintain they will not contribute to any accurate analysis of a person's type, and hence not tell you anything about Dom/Aux placements. You're always forced to "feel out" the person's 4 letter type if you maintain the strict, "only 16 kinds" of cognitive process breakdown, which most on this board do.