"So out of curiosity, and it is genuine curiosity at this point, if the GM is supposed to
a) run the story
b) be the antagonist"
Well it's more or less the same. Why? Because in literature definition of the antagonist is not a bad guy, just someone who brings the change to protagonist life. And that change with reaction to it IS a story. Nearly every story ever created. And yes protagonist is reactionary character by it's nature. But still as important. You don't have the story without the conflict, it just doesn't exist. Antagonist doesn't have to be a person in that matter, it can be a force of nature.
The story itself is a struggle. What side that brought the conflict, and side that deals with it. Rest is more or less decoration.
It works in every storytelling really.
Funny thing, in day 4, until now, Marcy is the antagonist. Of course in the scientific sense, not one we use day to day.
"c) carry the narrative"
It goes from what you have above, adding narration.
"and d) incite any and all interaction between players...."
No, that's not GM's real work. What you wrote is part of completely other role. Meaning reacting when something doesn't work. In this example for some reason characters didn't interact with each other, had no reason too. Meaning there was no story yet. Nothing changing the life of protagonists making them to move.
You could say that they should because a good character has it's own ambitions, plans. Even if it was true, when it's really not such plans doesn't really concern the game most of the time. Simply because player creating the character doesn't really know the game that well before he starts playing it. So even doing something the plan may be very easy to achieve, after a second post, or simply impossible with the state of the game. Such plans does not consider other characters, because they are rarely known before the game with enough detail.
"What exactly are the other characters even there for? Why would any player--in this case the GM--bother maintaining a game in which he/she is the only contributor?"
The story needs two sides. The characters here are the protagonists and as such are essential.
There are two ways of running the game really. Translating from polish rail road, and sandbox (I'm not sure if that's exactly how their named in English).
In first you have mainly a story to tell. You create mainly what will happen. The place isn't that important, needed mainly as background for the story. It doesn't have to be bigger than player eye can see. Here the challenge for the GM is keeping the character the centre of the story, and making his actions matter. In cRPG it would be Planscape Torment, or Mass Effect.
The second is mainly a place to be explored. Players just create characters, and discover toys laying around by themselves. Here hard part is making it move. There are two ways for that. Making toys interesting, thanks to which characters start having their plans about it, and in the end creating conflict with other players over them. In cRPG it would be Skyrim, or Follout.
Both rarely exist in pure form. Their just extremes on the scale.
Funny thing about the sandbox is that well done doesn't need the GM at all. True it's hard I saw it works twice in my 15 years of playing and running the games. And in second, where I was GMing I still needed to react once or twice.
"GM very little time to actually play."
Yes, because GM is not a player. Those are different roles.
In so called "new wave" of RPG it's a common theme to distribute GM role among all the player's, but then main part is clearly saying who gets the last word in what.
"there is only one person doing all that work"
Well GMing is a different kind of fun. It's like two hobbies one is creating beautiful wooden figurines, and second is playing with them. Both are valid, and entertaining, just for the different reasons.
First gives you satisfaction of creating, fun of endless possibilities. Second is restricted in what you have, simple, but still fun.
"There's nothing easy about a GM being "God" and "Satan" in the same game. In fact, its actually sort of boring, as well as strenuous."
Well seeing as God is all mighty power that created everything, and Satan is one of his henchman that just mixing thing up a bit then well it's just nice way too illustrate what running a rail road is all about. And well it can be easy. Although I know few GMs, that doesn't find themselves in this style.
I'm personally more in the middle. For me those styles are tools used whether I have a story I want for player's to experience, or just incredible place I want them to dig into.
"An rp of any kind should never be one person writing a story while countless others watch."
That's for sure. Story must always take into consideration the direction that character is pushing it. No matter the style. And it needs a good reason to go in the other. Or it will be irritating and boring for the player.