@Manbearcat
I think I agree but we'll see.
If fiat is used to force outcomes based on stuff like, what the GM wants to happen, to keep the plot moving, to provide a challenge. Then I agree that that specific approach isn't conducive to challenge based play. The correct attitude would seem to be something along the lines of 'you're not here to win (or entertain) but to see if the players can overcome stuff as fairly as possible and according to your best judgement.'
Which isn't enough alone but it's the guiding principle by which subsequent procedures and principles are judged.
To give an example using the 5E alarm.
The party is being pursued by Henrik Headhunter but they need to go into the Dungeon anyway. The Mage sets an alarm at the entrance. The GM must now use fiat to decide whether Henrik triggers the alarm when he enters the Dungeon after them. They could for instance decide based on some combination of what they know about Henrik and how cunningly they judge the alarm to be placed. They know Henrik is smart and capable and they don't think the alarm was cunningly placed and there is at least a possible way for Henrik to avoid it and so Henrik slips past undetected.
That's a case of fiat use that illustrates, to me, why you'd want to play a challenge based RPG.
So if you're saying the fiat in the Henrik example is bogus then we have a disagreement. If you're not then we might just by taking past each other. I agree that all the examples you gave were non-conductive to challenge based play but the above might get to the crux of it.
As an aside, for whatever reason, this didn't come up in my mentions. Headscratcher.
I think we're on the same page here. What you've written above is pretty much where I land. However, what I would say is the following:
* A game that features challenge-based priorities as its apex interests should be situating its GM so that they are (a) compelled to generate interesting, multivariate decision-points at each consequential moment of play (which should be most moments of play) and then (b) arming them via system to bring about those same complex and provocative decision-points. Finally, if the game is interested in a strategic layer (many challenge-based games very much do, but not all), then (c) the throughline of play should reflect that. Put another way, the moments of decision-points should stack in a coherent way, via the system and the GM working thoughtfully in concert, to create viable opposition to player goals. At the same time, the player's longterm considerations, decisions, mustering of means and management of system-levers should be able to be qualitatively evaluated as more or less skillful in gamestate management (in contrast with an alternative regime of play).
* To take your specific example, it is very much preferrable to me when it comes to challenge-based priorities for a system to eschew GM decision-making when it comes to the very important question of whether the gamestate is positively impacted (positive here meaning player's move made is successful and that success feeds into subsquent situation/obstacle-framing) which then feeds into the framing of subsequent play. So we need to find out if the PC Wizard's Alarm spell at the opening of the dungeon is foiled or triggered by NPC Henrik Headhunter? Cool. Here is some (much more desirable to GM fiat in this case) scheme of systemitized resolution:
GM: "Alright Wizard, I need you to set the value of any
vs test for your Alarm. Roll Arcana."
Player: <Wizard player feels like this is important so the muster some currency, spending it in a wager that the dice pool amplification will in turn amplify their Alarm spell> "I got 5 successes! I pour half of my vial of quicksilver and pouch of pixie dust (perhaps that is 2 out of 4 supplies) carefully along the periphery of my Alarm spell, enriching the magical field with those arcane contents!"
GM: One of the obstacles here is Henrik Headhunter's pursuit. Now we resolve Henrik's portion of the vs test. GM rolls Henrik's Dungeoneer 8 (rather than Hunter 10 as, let us say that Dungeoneer is the overcoming of traps laid rather than stalking and trapping) vs those 5 successes. GM doesn't like the odds. Henrik is capable and it would be desirable for him to maintain his stalking status of which the Wizard's Alarm going off would foil (and perhaps harm Henrik in some way, pending how Alarm is written in this prospective system). The GM decides to muster and spends some of Henrik's limited currency for the test; gains 2 more dice for 10.
Henrik generates enough successes to foil the Alarm. Now, rather than asserting the conflicting fictions (who is more capable, the Wizard or Henrik?) and subordinating the question of control over the gamestate (the question of gamestate control is the central piece of challenge-based play afterall) to GM discretion, we spend some of Henrik's future resources (thereby lowering his capabilities in conflicts to follow) to help enshrine the fiction that (a) Henrik is just as shrewd and capable as we imagined him while (b) managing to maintain the integrity of the question of gamestate control via authentically resolving this collision by way of system and participant decision-making around the tactical and strategic layer of play.
Circling back, maybe the system isn't particularly robust such that it can handle all of the above in such a fashion. Maybe it requires GM discretion. Ok. But the reality is, that is a decision around gamestate impact/control that the GM is asserting via fiat when an alternative model that doesn't subordinate that very important question of gamestate impact/control (which doesn't just impact this particular moment of player, but reverberates forward into subsequent play) might be available. I think it is trivially true that integrity of challenge-based priorities is far better maintained one way vs the other. I'm not saying resolution via GM fiat utterly cripples the integrity of challenge-based priorities, but...it definitely harms it by contrast at a minimum. Further, the more you stack these moments, the more harm to the integrity of the question of gamestate control you're generating.
The same phenomena can be seen in sports where a referee's judgement call (like the Strike/Ball call in a 1-1 count with runners on base in Baseball or a Defensive Holding call on 3rd and 7 in American Football) in a particularly gamestate-sensitive situation will reverberate into future gamestates and the more you stack those, the less "the game is being decided on the field" as the adage goes.
Hopefully that makes sense and clarifies our overlap and the potential daylight between us.