The point is that, for most of your Xs, no games do X. When asked to provide examples of RPGs that do X, you can't. Because there aren't any.
Your generalisations are just fantasies, ideas that you make up that don't relate to actual RPGs that actually exist and that people actually play.
Who said "Oh wait, that is not what the rule means!"
For instance, I quoted rules to you which give the GM two main jobs: presenting situations that are based on player-authored priorities for their PCs and narrating what happens when a player fails a roll for a declared action, making sure that that narration negates the player's intent for the action they declared. So of course if you describe the GM as having only one of those jobs, you're wrong!
Apocalypse World and Dungeon World also give the GM two main jobs: say something when everyone else looks to you to see what happens next, and say what happens when the action resolution rules call on you to do so. They also tell the GM that they should generally say something that is a "soft move" - a setting up or presenting of a threat or consequence - and should make a "hard move" - that is, bringing home a consequence - only if (i) the players roll 6- on a player-side move, or (ii) the GM has made a soft move and the players have ignored it, allowing whatever consequence was threatened to come to fruition.
You'll see that there is a certain similarity between the jobs of the Burning Wheel GM and the AW/DW GM, although they are not identical.
Now, we all know that you don't like a RPG that gives the GM those two jobs, but not other ones such as tell the players what their PCs should care about, tell the players what happens when they succeed on a roll, tell the players what actions they may declare for their PCs, etc. But that shouldn't make it impossible to describe the RPGs that you don't like with at least some degree of accuracy.
My point is that there is some RPGing where a comparison to crossword puzzles makes sense; and there is some RPGing where it does not. So, for instance, it would be odd to sit down and solve a crossword puzzle that I wrote; but it wouldn't be odd to sit down and play a tune that I composed. Nor is it unusual to try and put to words an idea for a scene, or character, or feeling, that I had in my mind.
My point being that solo Ironsworn is therefore not that bizarre, because it is not much like trying to solve a crossword puzzle.
I don't know what this is referring to. I can't remember how long it took to frame the situation involving the Falcon's Claw, have the player declare their PC's action, resolve that, have me narrate the upshot, and then for the implications of that to sink in. More than thirty seconds. Probably 10 to 15 minutes of play?
That last sentence is false, because it's not the case that, in RPGing, the only two options for players are to follow the GM's breadcrumbs or else do random things.
The player, as part of his PC build, wrote up a bit of backstory. That backstory included that the PC had lived with his brother in a tower in the rugged, arid hills - given that we were using Greyhawk as our basic map, geography and history, I suggested this was the Abor-Alz. The player found a picture of the tower online (I think an old castle in a relatively arid part of India) and emailed it around.
At a certain point in play, the PCs found themselves passengers on an Elven vessel sailing on the Woolly Bay. As a result of some failed interactions with the ship's captain, they were set ashore on the edge of the Bright Desert. After various hijinks in the desert, they set out for the Abor-Alz and the PC's old tower. When they got there, as I have already said, the PC looked for the Falcon's Claw. The failed Scavenger test meant that he failed to find it, instead finding the Black Arrows.
Notice that none of the action declarations I describe the players taking are random. They are quite deliberate, responding to what the players, as their PCs, know about their environs and circumstances. Notice also that none of those action declarations follow the GM's breadcrumbs. The players decided to have their PCs do whatever it was they tried to do with the Elven sea captain. (This was some years ago now, so I can't recall those details.) They decided to have their PCs enter the desert and get up to hijinks. They then decided that their PCs set out for the tower, which they knew about because it was part of one PC's backstory. And then the decision to look for the Falcon's Claw also flowed from that backstory.
Because the test to find the Falcon's Claw failed, I had to make some further decisions about it. The players had already been dogged, in their journey to and time at the tower, by a wastrel Dark Elf. (A Dark Elf in the JRRT sense, not the Vault of the Drow sense.) So I decided that the Dark Elf had the Falcon's Claw in his possession, having looted it from the tower at some earlier point in time.
So, the DM saying "We find the Claw" is your preferred approach: if the players say the right magic words (eg "We look under the Old Elf Tree" while having declared the actions that oblige you as GM to agree that their PCs are standing at the Old Elf Tree).
The players just saying "We find the Claw" is not a part of any RPG that I know, so I'll ignore that.
In Burning Wheel, the player can declare "I look for the Claw" when the framing makes such a declaration make sense (eg the player's PC is back in the ruined tower where they last saw the Falcon's Claw), and the rules then dictate how to resolve that action. I've already posted an example where the result of the declared action was that the Falcon's Claw was not found.
So, upthread, (3) was this:
But now (3) has been re-characterised, as the utterly banal "The DM makes the werewolf den if some game procedure dictates that they should". Surely even you can see that your two versions of (3) are not the same!
All RPG fiction is authored by someone. It doesn't become less authored by pretending that it's not.
As @hawkeyefan said, the players don't try and solve the mystery "for real". They don't set out on an expedition, carrying food and water and picks and shovels, looking for Old Elf Trees.
What they actually do is tell the GM about actions that their PCs take, and the GM then refers to their map and notes and tells the players what their PCs see and experience as a result, and the idea is for the players to build up enough information about what the GM has written down in the map and notes that, eventually, they (the players) can declare an action which will prompt the GM to tell them "OK, so now you're at the Old Elf Tree".
So the focus of play is on the players learning what the GM had in mind. As you said, it is a bit like solving a crossword puzzle.
Playing Burning Wheel or Apocalypse World or Ironsworn is not like solving a crossword puzzle. The whole orientation of and aspirations for play are quite different. In the puzzle game, for instance, it's of purely instrumental interest to learn that a certain NPC - a PC's brother - crafted Black Arrows before being possessed by a Balrog. In Burning Wheel, this sort of dramatically and emotionally impactful revelation is what we are playing for.
This is a particular odd comment, because rules for thieves reading strange language (and thus translating strange symbols) have been part of D&D since at least the late 1970s. There have also been magic swords, spells and the like as part of the game for just as long which permit translation to happen without even a dice roll being required.
