Other than the parts where the DM decides it all, no nothing specifically says, "The DM can gate behind proficiency." The DM decides the answer to whether it's impossible covers it completely, though, so they didn't need to spell out all the different ways that the DM decides it all.
Because I don't have to know them.
DM: "If you are proficient with Arcana, give me a roll."
I don't care what your modifiers are. I just excluded everyone without Arcana regardless of their modifiers.
Again, the DM gets to decide whether something is impossible or not and there are no restrictions on that, so if a DM decides that something has to have a chance of success or it's impossible for that PC, then that's what it is.
Page 237 of the DMG
"When deciding whether to use a roll, ask yourself two questions:"
"If the answer to both of these questions is no, some kind of roll is appropriate."
It's right there in black and white print. The DM asks himself two questions and then answers them himself. End of story. Nothing in the DMG says what the DM has to find possible or impossible, and the fact that they give a ridiculously absurd example of trying to hit the moon with an arrow shows that they aren't trying to force DMs down a path. I don't have to have a PC trying to jump the grand canyon to rule a jump impossible. I can in fact say no to a mere 40 feet if I want. I can say that you have no chance to make a 25 foot jump if you aren't proficient in athletics.
I can use any criteria I want to answer those two questions that I ask myself.
I wasn't saying anything here about whether DMs are permitted to do what you're describing (that is, to choose not to call a roll on the basis of proficiency). I misunderstood you, if that's what you were talking about.
Here's what I'm talking about:
A PC wants to attempt a very hard task (DC 25). It's not
impossible that someone could succeed at this task; indeed, other members of the party could succeed. But the PC doesn't have a shot at it, because their modifiers can only get them to a +2 (and no one has provided bardic inspiration, etc.)
Some have argued for the following position: according to RAW, the DM
should never call for an ability check in this situation, because a nat 20 would fail. In other words: if a nat 20 would fail, the task is by definition impossible for this PC and the die must not be rolled.
One implication of this position is that the new "nat 20 auto-succeeds on ability checks" playtest rule is entirely superfluous except as a pedagogical redundancy to eliminate a persistent misunderstanding, because DMs should never call for any roll that this new rule would affect in any way.
AcererakTriple6 has expressed this position very clearly multiple times. You wrote some things that made me think this was your position, too. Perhaps I misunderstood.
This is a separate issue from the question of how much latitude DMs are granted in determining what qualifies as impossible. Indeed, if the position I'm arguing against is adopted, it amounts to a
constraint on how DMs should rule what qualifies as impossible: the position is precisely that "impossible"
must include every ability check roll in which a nat 20 would fail.
My position is: RAW
do permit ability checks to
sometimes be made even when a nat 20 will fail.
It has nothing to do with whether DMs are also permitted to say to some players, "If I permitted your PC to make a check for this, a nat 20 would succeed; but it is impossible for X or Y reason, so I won't permit it." Clearly, they are not only allowed to do so but should do so for some X's and Y's. But there's very little guidance in the RAW on what "X or Y reason" can or should be here, and there is certainly nothing to indicate that "X or Y reason" must include "because your mods aren't good enough and a nat 20 would fail, even though the task is possible in the sense that other PCs could succeed."
