Personally I don't see it.
In Free Kriegspiel, there is a shared goal, in a teaching/training context, of doing a thing well. An expert in that thing helps with the teaching. In some ways it's like when I judge a moot, and I use my knowledge of law and legal argument to pretend to be a judge and put the student advocates on the spot.
The students can get better by going off and studying more law and more advocacy. And I'm a better moot judge now than I was fifteen years ago because I've had more experience and training of my own.
Likewise, the junior Prussian officers can go off and study more, speak to other more experienced soldiers about their experiences, etc; and then they will do better at Kriegspiel.
Both the wargaming and the mooting can work like this because there is an external reference for adequacy: the real worlds, respectively, of warfare and of legal practice.
In the D&D case, what is the GM an expert in? What is the external reference that establishes criteria of adequacy? How does the GM know better than the players what will happen if you strike a bronze statute with a war hammer, or if you try to seek an audience with a noble, or if you prey to Corellon in Orcish?
All we really have is the assertion that the GM should enjoy authority over these things. Cloaking it in the language of expertise is just misleading.