Your theory makes the positive assertion that there exist three mutually-exclusive categories of game (or three “agendas,” but we are trying to avoid jargon here). But, fine, if you would rather I provide a counter-example, I can do so. Jumping off an earlier post of yours from this thread:
It does not. This persists, and I've already addressed it twice before in this very thread.
GNS is about player agendas -- what a player wants from a game. You can have whatever agenda you want with whatever game, but you may not get well served. Some games do intentionally specialize in serving an agenda -- hence Story Now games. Most games can serve two agendas in some form. No game really serves three. Games that serve multiple agendas either have mechanics that can be drifted to better serve an agenda or they have toggle points where they switch. 5e is an example of the latter, where it is mostly about simulating the GM's story, but when combat happens you drop into more gamist subsystem. This is often referred to as the "combat whoosh" and is a noted shift in emphasis.
So, no, games are not exclusively one or the other. People aren't, either. The exclusivity point of the theory is only that, in a given moment of play, you cannot serve more than one master as primary emphasis. I agree with this, as it aligns well with my experiences from both before and after I was aware of the theory.
So first of all, I would posit that challenge is in fact an extremely effective way to hilight questions about the character, what they believe, and how they act when push comes to shove. In fact, challenge is essential for that purpose - you can’t find out how a character acts when push comes to shove without pushing and shoving them. Challenge and character must go hand-in-hand by this definition of character.
It's not, because the challenge here is referring to challenging the player. This is a player agenda, so they're the ones looking to get this from play. In the challenge mode (gamism) the player is looking to be challenged in their play, to deploy skillful play, and to be able to conclusively win or mark points. Losing has to be available as well, for the challenge to exist. This isn't at all about character, and the challenges that address a character's dramatic needs, or the things that the character defines themselves around, aren't this same kind of challenge. What's happening here is taking a word with multiple meanings and connotations and using that to blur and shift meanings and add ambiguity. It's one reason why jargon can be extremely helpful because it prevents this kind of misunderstanding.
Furthermore, verisimilitude is essential for certain kinds of challenge. Particularly, when the challenge is focused on “player skill” - that is to say, challenging the player to interact with the world primarily through narration with minimal mechanical resolution. Such challenge requires that the player have a reliable understanding of the fictional world and how it operates. The world needs a set of rules the player can understand and manipulate, which is most easily done by having it work as closely as possible to how one would expect things to work in the real world, except where deviations are explicitly stated and their rules clear and consistent.
No, it's really not. Combat in 5e can be very challenging -- it can scratch that gamist itch if done well. But to enable that, hitpoints are a huge part of that challenge -- skillfully managing this resource. But there's zero verisimilitude to hitpoints. If you dig into any class of thing you're going to assert, this duality shows up. For things to be about challenging the player, they don't also need to be firmly rooted in the believability of the game world. In fact, they often are only given a passing relationship.
And this brings out another good point -- we're talking about what's most important and not saying that multiple things cannot be present in any form. In a challenge, verisimilitude can be present to the extent it doesn't detract from the challenge. The moment that a need to maintain verisimilitude steps ahead of the presentation of challenge, you've switch priorities. The simulation is being served now.
It is of course possible to play games that prioritize one of these three goals over the others, but they can also work hand-in-hand, and personally, I find games where they do to be by far the most enjoyable.
I'm not aware of these games. Like, seriously. The best I've seen are games that hand things off between priorities in a pretty good way. Blades in the Dark does this, with strong Story Now play but also room to move into some skilled play challenge orientation, especially with managing the strategic side of the game (which, interestingly enough, intentionally and clearly steps away from the story now engine that scores run on).
Certainly, these two different interpretations of hit points are incompatible. However, one can prioritize verisimilitude and still not subscribe to the HP-as-meat interpretation (in fact, I, as someone who does care a great deal about verisimilitude, strongly dislike HP-as-meat because it creates what I would consider intolerable breaks from reality). Similarly, one can prioritize challenge or character and subscribe to the HP-as-meat interpretation. These interpretations of hit points are really not that strongly related to these three gameplay priorities.
I'll let one of the adherents to hitpoints being meat (or at least some meat) argue this with you. It seems clear that they have strong opinions, and this feels like dismissing them to win the point.
You can also achieve challenge by completely ignoring encounter building guidelines and just throwing things at the players that are well above their level. And this is only speaking of combat challenge.
Nope. This isn't challenge, because it's not addressing the idea of skilled play well. You might do this by adding a clear subset of mechanics and practices about how players can learn about upcoming encounters in a codified way (the player has to be able to leverage system and resources, not rely on GM grace), but 5e really doesn't have these features. On the other hand, a game of "see how long you can survive" does offer the ability to compare points, as it were, at the end, so that can work -- randomly roll some monsters and go. If that's your bag, go for it, but you're pretty explicitly tossed any consideration for verisimilitude out the window here, and certainly any story now, so I'm not sure this helps your point.
But unbalanced, verisimilar combat encounters can be a major part of a game that focuses on exploration challenge.
This actually sounds like a full on simulationism agenda statement. You're again using challenge in an ambiguous way (not intentionally, I think). The intent here is clearly verisimilitude, in that verisimilitude will be the deciding factor if there's a conflict. That a challenge (and not an agenda prioritizing challenge) will be present doesn't change this focus.