You state that the DM is the impartial one at the table - why? If I DM a game at my house, and thus by your definition am the impartial one, then I go over and play at Hawkeye's table, why would I suddenly become biased?
And why are accusations of bias exclusively the domain of players acting as arbiters? Can't a DM arbiter be accused by his players of being biased against them? Or just as badly, FOR them? Why are accusations against player bias worse than accusations of DM bias?
The DM in his role as monster/NPC player (if he is truly playing competitive against the PCs while wearing this hat) is just as capable of bias as a player playing a PC. Now maybe at YOUR table, the DM is the person most capable of resisting that bias - but it has nothing to do with the job - rather it is based on the individual traits of that person.
Big Story peeps might have a different view because Big Story DMs are more focused on fun, story, and adventure than on Big Challenge.
Can a DM be accused of it? Of course. Anybody can accuse anybody of anything. It's also possible that the DM actually
is biased. But that would mean they aren't playing the game properly. The DM is supposed to be an impartial and unbiased referee, among other things. If I sit down at another table, my expectation is that the DM is impartial, and won't give a second thought to it unless something happens that would lead me to question it.
The monsters and NPCs are absolutely not impartial. Part of the job of the DM is to play them appropriately, with all of their flaws. If the party is fighting 1e barbarians, then the barbarians attack anybody wielding magic, because they hate it. But playing an NPC or a monster doesn't make a DM impartial, biased, or competitive. The DM is not competing with the players. The monsters and NPCs probably want to kill the characters. The DM doesn't have a vested interest in them doing so. Thus, no bias.
More importantly, its about not having a bias between players/characters, not between the adventure and the players. That is, the DM doesn't show favoritism to one player or character at the expense of another.
I'm not accusing the players as being biased. They are. If you are a player at Hawkeye's table, you have a vested interest in your character over the other characters.
Does that mean you can't be an impartial arbiter? Of course not. But it can complicate it. It's more dependent on the group of people at the table. Making rulings that are beneficial to your character aren't necessarily biased. But they may be perceived as such by the other players. By not having another player as the arbiter, you avoid such problems.
Regardless, that's not the question I was answering. The question I was answering was:
But, if we do assume that such an adjudicator is necessary, why exactly must it be the storyteller? Wouldn't it make ALOT more sense for the person most knowledgeable about the rules to be the one to adjudicate them? In my experience, the person telling the story is usually -not- the one most knowledgeable about the rules. Yet, the default assumption is what he says about the rules goes. Why is it that way, and should it be that way? My answers would be "tradition" and "no".
And specifically the portion in bold. My answer is because it's D&D, and in D&D that's the job of the DM. To be an impartial and unbiased referee.
In 5e, it goes so far as to label one of the roles and an entire section of the DMG as "Master of Rules" and states, "Dungeons & Dragons isn't a head-to-head competition, but it needs someone who is impartial yet involved in the game to guarantee that everyone plays by the rules. As the player that creates the game world and the adventures that take place within it, the DM is a natural fit to take on the referee role."
I don't consider instructions within the DMG of pretty much every edition that part of the job of the DM in D&D is to be an impartial rules adjudicator, "tradition" or a "default assumption." It's the rules.
Should it be that way? In most cases I'd say yes. Keeps things simple. But it certainly doesn't have to be. It has nothing to do with Big DM, Little DM, Big Challenge, Little Challenge, or anything else like that. It's simply the design of the game. No judgement. No accusations. Just acknowledging the rules as written, and the reasons they've given for those rules over the years.
As always, use whatever works for you and your group.