If the presence was established prior to the party getting to that spot and rooted in the fiction, then the player will fail. The DM cannot just pop an anti-magic field into place and then coble up some fiction to explain it.
Where does it say that the DM cannot do so?
The DM decides it ultimately, but the player should have a very, very good idea in advance.
Should implies an obligation. Where is this obligation rooted? Is it in the rules, or does it exist only in the social contract?
I mean, why would the 1st level wizard think that he could climb the Cliffs of Insanity when the best climbers in the world have been coming for generations and failing. Nobody has successfully climbed it yet. If they're lucky, they are able to climb back down and live. If not...
Okay. Now take this answer, and apply it to the next three things the party attempts for reaching whatever they need to reach beyond the Cliffs of Insanity before the Wizard proposes
teleporting up there using some magic reagents the party acquired earlier. "What makes you think you can survive the trip through the Fire Swamps?" "Do you really want to risk an encounter with the Dread Pirate Roberts, who has notoriously destroyed every ship trying to sail through the Strait of Nightmares?" "You already heard the rumors in the bar about the vicious six-fingered man indiscriminately killing travellers on the road and in the forest on the long route around the Cliffs and Swamp. Even the Countess' soldiers, who have been exploring the forest on foot, have suffered heavy casualties." Etc.
That one is more difficult, but presumably there were ways to find out if it would be possible or not through roleplaying with him or others. The player should still have a very good idea if it is possible or not.
As above: where is this "should" rooted?
What is that proportion? I think it's rare for a DM to tell a player, "No you can't climb that easy to climb wall, because I say so."
Indeed, you are correct that such blatant and frank behavior is rare. But it need not be so frank. A "thwarter in chief" can come up with all sorts of reasons, to give guise to them saying no which "justifies" them doing so. I gave some examples of this way upthread. Sometimes it manifests as railroading, e.g. "We need to get to Darmir-upon-Pyne, let's go check out the cost of renting horses." "Remember how I mentioned the Countess' soldiers were on foot before? That's because there's a horse plague affecting this area. Even if a horse is healthy it isn't being let out for fear of it dying or spreading the plague." "Okay, how about we check in with the mage tower and see if we can teleport like we did to get to Lyonesse, beyond the Cliffs of Insanity?" "You used up the last of your reagents last time and don't have the money to get more." "Alright, I guess we have to go by boat then?" "There are several boats in the harbor, you probably have your pick of the litter...."
Other times it manifests in even more "covert" ways, like technically letting something happen but setting an impossible DC or, as was the case with the Rustic Hospitality example,
saying that it works and then denying any meaningful benefit that its use would provide. Other similarly covert MMI can include making all roads lead to the same answer or allowing something to
seem to work for a while before slowly introducing problems that eventually become insoluble, so the players are forced to switch tactics until they eventually happen upon one the DM approves of (note, it need not be one
specific tactic!)
The very first time I sat to play D&D, it was understood the GM had the ultimate authority over outcomes. But felt very much like I had complete agency because the GM used that authority to help make sense of the choices I was making (so the effect felt very much like I could try anything I wanted to in this setting).
Understood by whom? Understood from what? As I asked Max above, where is this understanding rooted?
What constrained the GM to only use their authority in support of your intent? What bound them to "help make sense of the choices [you were] making"? What prevented them from telling you no when you attempted things?