I don’t think those logically follow from each other, although I agree some people go that route. As evidence, I would offer
Kriegspiel, which was a war simulation used for training real officers by the Prussian Army very successfully. It is most definitely a simulation with no need to consider gameplay / enjoyment or story yet it was mostly operated by the referees judgement based on experience. It did not have a whole stack of specific rules or procedures for different kinds of activities an army might undertake. Hence simulation does not need to mean lots of rules.
And there is a through-line of Kriegspiel > Braunstein > Original D&D so I would consider that relevant to the topic of RPGs.
I'm aware of the history here. Among a dozen or more other books I've read Peterson's "Playing at the World", Fine's "Shared Fantasy" and Dunnigan's "The Complete Wargames Handbook". We can assume we are both very familiar with the history of games and the development of roleplaying games in particular.
That said, I think you are misunderstanding the role of the Umpire in Kriegspiel and understating the degree which as Kriegspiel evolved it more and more followed the path that I'm describing.
First of all, it was not the primary role of the Umpire in a game of Kriegspiel to decide the rules in the way we would think, nor was the refereeing deciding things like "in my opinion cavalry here would be successful" or how many units a cannonade removed. They had rules for that the Umpire was expected to apply. The primary role of the referee was to "roleplay" the troops that the player was pretending to command. In Kriegspiel the player (realistically) did not directly control his army like a puppet. Rather, the player wrote down his commands and "sent them" to his officers, and it was the job of the Umpire to interpret how the officer would receive and act on the order he received. This was to teach clarity in issuing commands. A player who wrote unclear commands or vague commands might find his units behaving in ways he didn't intend. That was the primary role of the Umpire's judgment.
Each edition of Kriegspiel brought with it more and more complicated rules to cover more and more situations.
As you probably know, "Free Kreigspiel" where the Umpire would dispense with the complex rules and just use his own judgment regarding whether a volley of fire from 500 yards would inflict significant casualties on a unit of cavalry rather than dicing for it was a reaction to the increasingly complex rules of the simulation. But, it was adopted not necessarily to make things more realistic, but rather because the military officers hated learning the rules and it was becoming increasingly hard to find people who were willing to devote the time to becoming Umpires. That is to say the real motivation here was in RPG terms gamist and not simulationist. So in fact, I would argue that enjoyment of the game was paramount in this decision. The games were becoming so hard to run and so lengthy to run that ardor for playing them was waning, so the Prussians moved to simplify the game by reducing the rules.
Incidentally, this was in my opinion a huge mistake because the Umpires are then always just fighting the last war. This would contribute to the massive failures of everyone to anticipate the realities of the first World War, and then later Imperial Japan overriding the rules telling them they had no chance of victory with the judgment of the Umpires that Japan's unique samurai spirit and will to win would overrule reality.
Not incidentally, when Kriegspiel jumped the Atlantic to the USA, the developments went the other direction than in Prussia. While Prussia moved to more "Free Kriegspiel" in the 1870s, in the USA developments continued toward simulation with more complex rules and more and more guidance to the Umpire in how to run the game. From an RPG perspective the most important of these as Strategos which is bewilderingly complicated in its tables and calculations.
And it was Strategos that Arneson was an expert at and which he had previously published variations for the Russo-Turkish war, the US Civil War, and most notably for our story Strategos A for wars in antiquity. And arguably, Arneson's game of Blackmoor was originally intended as a complex metagame (itself a highly detailed simulation) for setting up battles in Strategos.