I think your analysis is excellent. You could call it "adjudicated vs legislative" or "common law vs. civil law" axes.

Imagine, if you will, that you are playing Free Kriegsspiel, and you are, in real life, an artillery officer.  The adjudicator is highly skilled in most matters of war, but since you are a specialist, it would be fair to say that your knowledge is more robust than his.  During the game, your cannons are firing up to 1500 yards (just under a mile).  However, you are in a position where you do not have infantry or cavalry and your position will be overrun by infantry currently 1.5 miles away.  It would matter very much if you can add extra powder to your weapons and strike the opponent further away.  Every 100 yards of accurate fire could realistically be another shot.  If double charges have a 2% chance of destroying your cannons, but can strike between 2000 and 2200 yards, it might very well be worthwhile under the circumstances. 

Now, outside of putting the game on hold and conducting a controlled experiment someone has to make a call.  The arbiter wants to be right, and while the player may have more expertise, they're certainly not impartial. 

In a perfect world, the player would have had a chance to update the rules in advance.  Effectively, the player and the umpire both know what the rules are and can agree what is and isn't possible under normal circumstances. 

I certainly think there's a point where rules can constrain the game unnecessarily, and feats are an example of that, but I don't think that attacking two different enemies twice in a round is an example of why feats are bad.  The rules (any edition) are actually very clear about how many attacks you get - asking for extra attacks ISN'T supported by the rules and 'judgement' in that case is sporadically rewarding players for asking.  Taken to the logical limit, it becomes a game of trying to convince the GM that the current circumstances are similar enough to another time when it was allowed.  The derogatory term for that style of play is 'mother-may-I'. 

While an RPG does not constrain action in the same manner as a board game, it does constrain action.  It turns out, you can't fly just by wishing you can.  You need an ability that gives you flight for that to be an 'allowable move'.  Ultimately, the difference isn't in whether a move is legal or illegal, it's in the scope of options and how rigidly they're codified.  In a board game you might be limited to how much you can move by the roll of a d6.  In OD&D you might be limited by your speed of 6".  Trying to allow for more actions (and codifying how an unexpected action should be resolved) is important.  Going back to the maze example, when the rules say 'you can't cross a chasm', that's very rigid - in D&D the rule is 'you can't cross a chasm unless you can find a way to do so'.  That might be jumping, or flying, or filling it in with debris or any number of other solutions - but ideally those solutions are actually knowable from the rules. 

The more you understand the underlying rules, the less constraining they feel.  In multiple editions of D&D I've had new players announce seven- or eight-rounds of actions on a single turn.  Finding out that you have to break your actions into discrete chunks of game-time isn't automatically intuitive, but it isn't actually CONSTRAINING - you can still do all those things, it just takes extra time and other people have a chance to react.  I wouldn't say that's the game rules defining the experience - part of the experience IS the game rules. 

There is no platonic ideal of an RPG with no rules (or rules only knowable by a referee).  In an ideal world the rules would be so easily understood and all players would have exactly the same idea of what is or isn't possible - but considering we're dealing with the fantastical and people are approaching it from different genres makes that pretty difficult.  A player that watches a lot of wire-fu may have a very different idea of what combat should look like versus a player that LARPs medieval combat.  Rules help clarify expectations and reduce arguments at the table. 

As you previously indicated, when something happens often enough, it gets codified.  With (at least) 5 editions, it just makes sense that more situations have come up often enough that clarity was needed.  Jumping on the back of the lumbering Oliphant and shooting it between the shoulder blades where it has no natural defenses may not have come up pre-LOTR, but it certainly comes up now.  Entering a creature's square, positioning relative to natural attacks etc are important enough that they should be consistent.  I don't know anyone that played OD&D and didn't have a binder of house rules.  The fact that the rules neglected to say didn't NECESSARILY mean that there didn't need to be a rule. 

Interesting theory, though I feel it takes quite a few liberties, despite WotC era books specifically saying and even labeling that adjudication and DM decisions are paramount to running a game, not to mention that the rules themselves are Guidelines to be used, changed, or discarded as the players (DM included) see fit. One thing you said stuck out to me in particular.

Quote from: Eirikrautha on July 10, 2021, 10:58:44 PM
When the mechanics of an RPG begins to limit player reactions to a situation, the game is starting to slide down the spectrum towards board game.  This is a fundamental difference between the earliest iterations of D&D and the WotC versions of the game (in scale, if nothing else)..

What, exactly, is the opposite? A players pre-3e has an opportunity to 'cleave' two goblins at once and says he wants to. The creatures are next to one another and the DM says "Ok". So, now that option is going to be used every single time that circumstance shows up. A "no" under the same circumstances ruins verisimilitude. So if "cleave" is fine, why not just say "I'm hacking off his head" against every opponent? What in-game reason is to limit that effect from occurring for 100% attacks? And this goes for Monsters too. Sure, the DM can say "no, because I said" but that feels hollow.

In the other spectrum, since I do play a lot of 4e, I've ruled a lot when it comes to ad-hoc adjudication in terms of player agency. I had a PC surrounded by enemies and he decided to tie his sword to a rope.and swing it around his head as a makeshift weapon. So, I looked at some suggestions in the DMG and ruled that he'd get a Whirlwind type attack (close burst 1) but couldn't use his proficiency bonus because he wasn't using the weapon in a proficient way and only did the normal damage (no ability score mod) but could keep magic bonuses. Ended up rolling well and killing 5 of the 8 monsters surrounding him before one of them cut the rope.

The difference here is that there was something to help this adjudication. The DMG had common damage expressions to look at and base off of that helped instead of going completely off what I felt at the time was good enough. This goes for a lot of things too. Again, I like using 4e as an example because I've DMed it often. Want to melt ice, use a fire power. Need to scare some locals? Use a beast shape power to turn into a bear. Want to create ice to walk across a pond, use Cold spells. Things like that. Not covered by the rules but in the DMG to make it fun.