We have what is claimed to be a 'mimetic' theory… that describes language "by mimicking its crucial properties” (Halliday 1996), a claim that the theory is more than just a 'model'.
It shouldn't therefore be surprising that the list exchange is as much interpersonal as ideational, if the theory can describe how institutional power relations are realised in texts, alongside the categories and relations of the theory.
Conversely, a claim that the architecture of the theory is independent of institutional power relations would contradict the metafunctional dimension of the theory. From the interpersonal perspective of the theory, such a claim would have to be interpreted as a strategy to manipulate institutional power relations.
In order to understand and perhaps reconcile our apparently incommensurate versions of the theory, Im sure we have to honour its breadth, and admit our own varying institutional positions. These include the focus of our specialisations on particular strata, as discussed earlier, alongside our personal affiliations (and antipathies) to supervisors, colleagues and institutions.
If we could acknowledge but tease apart the personal from theoretical, perhaps it would be possible to admit that genre, register and discourse semantic theory may indeed mimick the properties of the system itself, although they may be unnecessary for the institutional work of many linguists.
 Halliday's claim does not assert that 'the theory is more than just a model'. Ideationally, language is an evolved theory of experience, and a linguistic theory is a designed theory of language; not just a model — a model. Given that language and linguistic theories are both semiotic systems, they both share the properties of semiotic systems, and it is in that sense that a theory which construes language as a semiotic system is mimetic ("mimics its properties").
 To claim that the (ideational) architecture of a theory — think of general relativity or quantum mechanics, for example — is dependent on (interpersonal) "institutional power relations" is manifestly absurd. Being ideational, the architecture depends on agreement with experience and logical consistency. It is the architecture of religious dogma that potentially relies on "institutional power relations"; for example, because the Catholic Church included the Aristotelian cosmogony in its dogma, the Pope had Galileo imprisoned and Giordano Bruno burnt at the stake for supporting cosmogonies that threatened their "institutional power". Cf Halliday & Matthiessen (1999: 618):
… the ontogenetic perspective shows that in fact our experience is being ongoingly reconstrued and recategorised as we grow from infancy to maturity. This is the outcome of processes taking place in human history — evolutionary events that are at once both material and semiotic, and that cannot be reduced to either purely physical processes driven by technology or purely discursive processes driven by ideology.
 It is precisely those of us who are outside the "institutional power relations" who are free to make public our reasoning without fear of recrimination, and who have nothing to gain from "manipulating" such relations, even if we were motivated to do so, or if such a thing were possible.
 Rose's use of admit and acknowledge harks back to a previous post in which he judged those who didn't agree with him as obstinate (and himself as capable); see an Appraisal analysis here.
 "Genre, register and discourse semantic theory" may well mimic the properties of language in some way or other. The problem with them is that theorising them as strata is inconsistent with the rest of the theory in which they are placed — and it is the rest of the theory that gives these theories their "institutional power". It is clearly this last point that Rose is so afraid of — the loss of "institutional power" — given his continual raising of the issue.