Thank you for stating the core question so succinctly. I've put forward a prescription (in the form of a manifesto) that takes notice of language often used and observes that - by simply taking said language sincerely we could find an answer.
I agree, and really it's not about those semantics. I like the efficiency of counting GM as player, but the crucial step isn't that efficiency; it's far more that
Emphasis mine, and it is the latter point that most compels me. To my observation, folk designing games like
@kenada are going to have to grasp that nettle. One way is to mark the contrast by stressing that the GM is a
player, in the sense
@pemerton has outlined. Folk recognise the ideological significance of that design move, as testified to by posts in this thread.
Take the manifesto like this - neotrad game designs ought to reposition GM by demarking them
player. At the least, a neotrad game text will contain rules that constrain and compel GM's voice in the ongoing negotiation of play... and GM cannot "rule zero" themselves out of that.
All of the following is relevant
For convenience, this is how I recognise a candidate game text: i) first filter for every game text I understand to fit a traditional mode of play (OSR, sandbox. sim, trad) and then ii) filter for just those that also integrated innovations from indie-games (largely storygames) with a particular concern for how they treated GM powers and centered player authorship. One will find games that ought to be neotrad. Observe them in play (find actual play of such games and observe it.) Where they do not follow the manifesto, the prediction made is that they will not in fact bridge the experiential space between trad and indie as Harenstam hoped. I've given the example of the Beneath Ash and Snow, Forbidden Lands actual play. It's good quality OSRish-sandbox play, but the imported mechanics are not - in the hands of a trad-GM - doing the jobs they were designed for.
What then are the principles of and jobs done by a neotrad-GM, if it is not enough to say they are a "player"?