@pemerton I'd like to lay out what I believe are our areas of agreement and contention, without preferencing any verdict
1) It's possible for a GM to function as a
referee
Yes, there are games - some of which are RPG like, some of which are RPGs - in which the "GM"'s function is largely that of referee. Free kriegspiel, Braunstein and Tomb of Horrors would be examples.
There are marginal cases here, and Tomb of Horrors provides an example: in an original play report (from Alarums & Excursions?) the player complains about how the GM adjudicated the rule that elves can notice concealed doors without searching for them. This is an example of what happens when there is no such thing as
expertise because the subject matter (here, the way that elves may or may not notice doors beneath a layer of plaster) is entirely fictional.
2) You contend that in some common modes of play (including trad and neo-trad) GM cannot function as referee
3) Among things that prevent GM functioning as referee by your lights are - a) when they establish truths about setting, b) when they act as a font of unnecessary obstacles, c) when they choose a resolution
4) You contend that 3a, 3b, 3c make GM functionally a player
I content that - to use Suits' terminology - that if a GM shares the prelusory goal of
establishing and jointly imagining a shared fiction for amusement then they are, by definition, a player.
A free kriegspiel judge does not have this prelusory goal. Their goal is
to provide as accurate as possible answers to questions about what would happen, were the modelled situation a real one. A Braunstein judge, as I understand it, has a similar goal. ToH, as I've said, is a marginal case but much of the time has something like this character.
To give a concrete example: a GM who decides that
NPC X does such-and-such a thing because that seems a natural reaction to what the PC just said do them is not refereeing in any interesting sense. They are not adjudicating the application of a rule to a player. They are exercising their "ownership" of one element of the shared fiction - the NPC - to make a contribution to the shared fiction.
The difference from the free kriegspiel judge, who uses their knowledge of actual battles and terrain to decide how the fiction changes if a player (say) has their cavalry formation attempt to ford the river, strikes me as obvious. The judge is applying expert knowledge, to reach an informed opinion, with the purpose of instruction. If they are
wrong in their estimation of how the cavalry would go fording the river, they are properly subject to criticism (by fellow judges, perhaps even by the players).
The GM, on the the other hand, is just making something up about the NPC. That it coheres with some other things they made up is neither here nor there for present purposes. It is not an expression of expert knowledge. It is not instructing anyone in anything. It is not subject to criticism as to its accuracy, by reference to an objective standard. I have no objection to nevertheless labelling the GM a referee as a purely conventional label (like Classic Traveller does). But the GM is not a referee in any substantive sense.
5) We agree that wielding rule-changing power may conflict with or disrupt the prelusory-goals/lusory-means/lusory-attitude (what I will call the lusory-fabric), that players must accept (perhaps on account of their being part of what it means to be a player)
6) You contend that wielding rule-changing power inevitably conflicts with or disrupts the lusory-fabric: there is no means of governing the wielding to keep it in compliance
Given that, by definition, adopting the lusory attitude means accepting the rules as constitutive of the activity to be undertaken, then rule-changing powers are a puzzle.
In the tradition that Suits is working in, there is a standard way of handling the puzzle.
For instance, is the power a chess player has to queen a pawn a rule-changing power? The standard treatment of it, rather, is to simply redescribe the rules that govern pawns and the rules that govern how the board is set with pieces to incorporate it as a rule - so there is a rule along the lines of
if a pawn reaches the end of the board then its player must remove it from play, and place in the same square their choice of rook, knight, bishop or queen.
Hart takes a similar approach in setting out the game of "scorer's discretion*.
I don't know the card game Mao beyond
@Enrahim2's description of it, but we could probably set out the "rule changing power" in similar terms:
under the appropriate condition, a player gains the following power: to imagine a constraint, keep it secret, and then - if another player makes a play that violates the imagined constraint - to declare that play invalid (or whatever consequence follows from breaching the player-introduced rule in Mao).
What would rule zero look like, formulated similarly. At first blush, it looks like
Under any conditions, this player may declare any other players move invalid; if pressed, they must either introduce a bit of fiction that explains the invalidity, or state a house rule or ruling that explains the invalidity. I contend that such a rule is not a lusory means in Suits's sense. Because in no sense does it establish a "less efficient" means.
9) I contend that 6) is false: that rule-changing authority can be made subject to the lusory-attitude through the proper principles and rules (and that on reflection, it will be seen that this is the only way games can function consistently at all)
No general proposition about "rule changing authority" seems warranted, because some of those can really be restated as rules that will count as lusory means. (See just above.)
I do not see how this can be true of "rule zero", however, as that is usually characterised.