Yes, this is a great description of my thoughts / doubts.
The only thing is, it's difficult to imagine a world where certain groups of people only strictly use one set of functions while others use another. The way I've always seen it is we all use all functions at different frequencies, and we subjectively try to quantify which ones we use more frequently and then pin a type crown on that tooth. I suspect that I have some blend of Ne/Ni/Te/Ti and phase between the two types, but my general pattern of behavior is best described by MBTI ENTJ / Soc ENTp.
I can catch myself quite frequently switching from Ti to Te mode and vice versa.
In an empirical sense, there is of course less rigidity in function order and composition, in that there isn't exactly a part of the brain that controls "Ti" and some other part that controls "Te" and another part that covers "Ni", and so on. However, it has been seen that a person's type and thus function order is reflected in part in brain activity, in that certain patterns exist for certain combinations of functions, with an important note that, for example, an ESTJ's and an ENTJ's brain activity aren't going to be as congruent as you might think with the dominant Te, because it really does matter what the other functions are. So in practice, it isn't as rigid as we might think, but there
are demonstrable patterns that correlate with function preference hierarchies (see Dario Nardi's research for more).
However, I will always say that this isn't cause for us to throw out the very insightful systematic understanding of function order we get from either Western writings or Socionics' Model A. I think what gives the theory strength is its internal consistency and in
some ways its rigidity. Because while I don't actually believe that every INTP/LII has the exact same cognitive processes that are clearly delineated in the brain as being some sort of "Ti, then Ne, then Si, then Fe" hierarchy, I think that using such as a model is very useful for examining what kind of information is involved and how it is processed. I will also note that I don't much believe in the idea of "Oh, I'm thinking about abstract topics, so I must be using Ti now" vs "Oh, now I'm thinking about the practical application of my ideas, so now I'm in Te mode" because such would imply that the cognitive process that is Ti is incapable of doing what Te does, or vice versa. I wouldn't even say that you "need" any specific function to complete a task, like Ni to visualize future likelihoods or Fe to be emotionally expressive. Whatever thinking function you have is still capable of thinking in a different way -- it just might not be your natural orientation, or your focus, or your strength. That's why I prefer Socionics' model of IM elements as determining what kinds of information you naturally tend towards, rather than what processes you're "capable" of using (and in their order of competence, to boot).
Indeed, if you examine the 8 function roles in Socionics' Model A, you'll find that an ENTJ posesses Ti and Ne in its Super-Id function block, indicating that though the ENTJ may be familiar with the two elements and be moderately proficient in their use, they do not prioritize them and at times ignore or marginalize the information that these elements are mainly concerned with.