Okay, I've done a bit of organizing thinking on this, and here's the rub: If you're going to use goal and approach as a method, you must present a game that offers handles to the players to propose goals and approaches. In short, yes, it's part and parcel of the method that you must change how you present situations. If you're only going to call for rolls for things that are uncertain and have a risk of failure, then it's incumbent on the DM to present uncertain situations with consequences of failure. This doesn't work if you just have hallways that may or may not be trapped, as what happens is that players are now asked to do repetitive goal and approach declarations and this gets old fast. It's easier handled in an ask-for-roll approach as the entire exercise in the fiction is abstracted and pushed off onto the mechanics to get past this repetitive play and move to the bits with heft.
Goal and approach require that the DM change the presentation of the game. You have to present challenges that prompt the players into action. This is different, as most games just have the DM present the description of the room and have other information gated behind the obligatory skill checks. You either gain the information or you do not, and this affects the actions your take and if the things you did not notice affect you and now call for new checks or if you engage what you have noticed via other checks. Goal and approach, though, doesn't work at all with this presentation -- you must provide a handle on the action for the players. As such, it requires a form of framing more akin to more narrative-style games where you present a dynamic situation with a clear call to action and then say, "what do you do?"
Yes, this method misses some of the things that the ask-for-rolls does -- they are completely different styles of play. What's missed, though, are the things that no longer make sense in terms of goal and approach play. I don't miss that my players ask for rolls, fail, and give me the opportunity to create new fiction to describe their failures because my method does this well, just in a different context. My method creates consequence based on what the players express rather then what I, as DM, think. I find this preferable. I have to do a bit more work on the front end -- I have to provide a clear call to action in my scene framing and this isn't trivial -- but I offload a lot of work on the backend as I'm now just reacting to the players and following their lead through the scene. This is very different from the much more DM mediated experience of asking-for-rolls and using rolls to gate information and provide tension. Both are very valid ways to play. Neither can recreate the experiences of the other. That's actually a big selling point for me -- most of my pain points with D&D came from the heavy DM load and I find goal and approach lightens that considerably and presents play that I enjoy very much. YMMV, and that's part of the coolness of this hobby.
(Bold emphasis added.) I acknowledge that the way in which you implement goal-and-approach requires the playstyle changes you describe, including the bolded part about scene framing. I disagree that goal-and-approach as (obliquely) described in the PHB and DMG requires those playstyle changes.
As evidence, I would point to the fact that 5e contains explicit rules for resolving repeated actions by using passive checks. Ergo, 5e contemplates that repeated checks may be a thing even though it also describes the basics of the goal-and-approach method. That suggests to me that goal-and-approach in its simplest form can't require a framing style like yours that precludes the possibility of repeated checks.
Lies are the traps of social interaction challenges. Telegraphing both gives the player a clue that something is up. Maybe players interact with the trap or the NPC's falsehoods based on those clues or maybe they don't. What they don't do is try to Perception check and Insight check their way to finding stuff that may or may not be there because there's a "gotcha" around every corner if they don't do their SOP. They can trust that the DM isn't going to present the game that way and that paying attention has a payoff.
Telegraphing as a technique, however, is something I would say runs alongside the players describing what they want to do and hope to achieve, since a DM needn't telegraph traps or lies for players to describe things like that. They are very complementary approaches though that together produce what I would say is a more solid, fair game since they basically represent the DM and player performing their respective roles in the conversation of the game to the utmost, that is, the DM describing the environment and the players describing what they want to do which both feed into the DM narrating the results of the adventurers' actions.
And this is why I think the term "goal and approach" needs to be defined solely as what I said it was a few posts up and some other name given to what are a host of techniques that when combined are greater than the sum of their individual parts. If we ever put together a thread on this as discussed earlier, perhaps it will make things a great deal clearer to those who actually seek clarity.
I think we're in agreement. I think telegraphing combined with goal and approach is better than not telegraphing and asking players their goal and approach. But I can't make the claim that goal and approach requires telegraphing, as it's literally just the player being reasonably specific about, well, the approach to a goal.
"There's a 40' hallway to the north" may well be something you'd hear in my game as I describe some part of the dungeon. It's just, in my game, players know that I'm not going to play gotcha, so they won't have to goal-and-approach searching for traps just in case. They can just walk down the hallway (approach) to get to the other side (goal) like the proverbial chicken crossing the road. Or they might 10-foot-pole it in an abundance of caution - who knows? I just know that I'm telegraphing to make it a fair game and that's all. What they do after that is up to them.
As an observation, it seems to me that the framing techniques @Ovinomancer considers to be a necessary part of goal-and-approach may be required specifically when one is trying to emphasize high-stakes, point-of-action action declarations. If I understand correctly, a low-stakes action declaration of walking down a hallway (approach) to get to the other side (goal) is undesirable at @Ovinomancer's table. It makes sense to me that if one want to avoid low-stakes action declarations one has to exclusively frame high-stakes situations. (I just personally don't see low-stakes goal-and-approach action declarations, like character movement, as undesirable, and therefore see no issue with describing a hallway as part of my description of the environment.) @Ovinomancer, if I'm misunderstanding, please let me know.
In any case, goal-and-approach clearly means slightly/somewhat/significantly different things to different people. (I mean, you and @Ovinomancer are disagreeing about whether you agree on what the concept requires.
