I decided against replying to Ovinomancer because I didn't want to get baited into a flame war. However this post goes a long way towards resolving at least some of the issues. It is the first truly clear communication (ironically) of the intended meaning of the term by those supporting it.
In particular, based on how I've seen it used, "goal and approach" is not a GM resolution methodology (despite what people conflate it with). Rather, it is, as you describe, a communication methodology. The GM resolution methodology is separate from, but dependent on (which is not the same as "determined by"), the communication methodology.
Goal and approach, as it appears to be defined by you, removes ambiguity on the input side of the GM resolution method. The GM uses the input to determine what resolution method to employ (eg: whether to roll dice, and if so, which skills to employ, etc), and from thence, the output.
The GM prefers the input to be as clear and unambiguous as possible, because that both makes his choices easier, and reduces the likelihood that the finalized resolution contradicts what the player was intending to do. This helps the game run more smoothly, and everyone is happier.
There are a variety of ways to make the input clear and unambiguous. Aside from explicit descriptions, use of the predefined structures of the game mechanics is a way of handling it (eg: the Fireball spell). Having the player indicate that she is casting the Fireball spell is using implicit, but unambiguous information. So my understanding that you were insisting on explicit information only is not true, at least for the version you present here.
However you still require explicit presentation where such requirements are problematic, such as Insight or knowledge checks.
Side Note: I will note that this is a particular sore point for me because of how certain GMs have dealt with Insight-type interactions involving characters whose entire shtick was built around social skills. So there is a fair bit of anger towards GMs that would dismiss certain player approaches as "not good enough", particularly when it seems like cover for the GM not doing his job at all.
In any case, a primary issue in this particular skill is that Insight is internal. It is a gut reaction; it is feelings; it is experience. It is not, "I hearken back to my days as a student and remember how the upperclassmen behaved." That's as nonsensical as requiring the fighter to recount his days studying under the fencing master Benetti before every swing he takes.
Rather, it is the ongoing analysis of everything you notice about a person. Eye contact. He's fiddling with his ring. The distance she's maintaining (too close? too far?). Subtle tones of vote. The limp that occasionally vanishes. A thousand and one details that the player will never know, and thus be unable to make use of. This actually compares remarkably well to combat, as any of these sorts of details could be relevant to a fighter attacking and defending in a fight. However the fighter doesn't need to justify the approach made with every single swing; he just says, "I attack." However the social character is apparently not allowed to say, "I use Insight."
It is relatively rare that there is a realistic "in the fiction" narrative that can supplant the simple request to invoke one's skill using the roll, mostly because GMs fail to provide the ongoing passive information that a character's Insight should be providing. Thus, in order to actually make use of a skill that her character is supposed to have, she must constantly pester the GM for Insight checks.
I usually shouldn't need to ask for an Insight check; if I do (aside from a specific thing I'm puzzling over), it feels equivalent to saying that the GM isn't doing his job. If I need to not only ask for permission to roll, but also come up with some convoluted gibberish to justify it, that feels like an unpleasant play experience.
This rolls back to the issue of "goal and approach". It requires that the communications be unambiguous, which is usually expected to be presented as explicit narrative, but may reference unambiguous mechanical elements. The problem is that this cannot work with respect to elements of play for which the player herself does not have the information necessary to make an unambiguous statement (or a mechanic that allows everyone to agree not to ask hard questions, such as combat or spellcasting), or for situations wherein the GM's resolution is necessary before any such narrative communication could be created in the first place.
In general, it would seem that goal and approach would work well for resolving actions, because actions are a thing that is done, and thus can be described as doing a thing. Certain activities and skills, however, are not "actions", and thus goal and approach is not suitable for interacting with them. The problem that I continue to see in the discussions surrounding this is the refusal to admit to scenarios where goal and approach is either not appropriate, or the problems that it would normally introduce are ignored. This may also be related to the assumption that "goal and approach" is a resolution method in and of itself, and thus considering it a fault of the player when the system does not work out as such.
