IMHO, the difficulty of answering succinctly is the answerer's problem, and the reader's problem. Writers need clarity and efficiency; readers need patience, motivation, and skimming skills. See my answer to this question to get some sense of where I'm coming from on the matter of complexity, length, style, and responsibility. As for the OP's responsibilities, I think we should focus on defining the banner text as is:
There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.
Too many possible answers is hard to disambiguate from the "primarily opinion-based" banner text:
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.
It's hard for me to imagine "too many possible answers" that would be based on facts, references, or specific expertise. I feel that we want answers to questions like these, e.g., "Why might people choose to get divorced?" but we don't want to feel obligated to provide every available answer, and we shouldn't. Therefore we could close a question like this for being too broad, or we could choose to add our own answers pertaining to whatever we feel is missing from answers so far. I don't see any harm in taking the latter approach, whereas I do see harm in the former. I would welcome any counterpoints on this opinion.
A more legitimately too-broad question is one that explicitly demands a complete answer or more answers than people can be expected to provide, such as, "Please list all the articles that cite Freud's (1915) The Unconscious." This question is not off-topic per se, nor opinion-based, nor unclear, so "too broad" seems like the right problem to raise with a question like this; no one wants to do someone else's literature review if it's not sufficiently focused.
This leads to lesser and more ambiguous varieties of the same problem, where the question is clear and focused on empirical cognitive science, but not a reasonable subset. I'm inclined to interpret "reasonable subset" pretty liberally, but I know others aren't, so expect this will have to remain a largely subjective, democratic judgment process. Fortunately, five votes are required, and people can always edit. I strongly encourage commenting in any case where the judgment feels even slightly subjective on the part of the voter, or at least voting on a preexisting comment that expresses the voter's opinion if it's already been stated in a constructively critical manner.
A relatively objective anchor for these judgments and a potential pitfall of liberal tolerance of broad questions is that, even if these can be answered partially and objectively, questions that are too broad are unlikely to receive answers that the OPer would
accept with the check mark and +15 rep bonus. The SE system wants OPers to accept answers eventually; it's a low priority, but non-negligible, and related to the breadth problem. If you think the question is worded in a way that makes a truly acceptable answer almost unfathomable, the question might be too broad. If you think your question will come across this way, or someone tells you that your question is too broad, it might be wise to include a little disclaimer saying you'll accept less-than-comprehensive answers. IMHO, people should feel free to provide less-than-complete answers in general, though we should probably at least acknowledge this choice explicitly. Doing so takes the pressure of a too-broad question off the answerer, and allows an incrementally useful response to be made, thus making the question useful. If the OP can be convinced to accept an answer after a reasonable amount of time, and a sufficiently decent attempt to answer it usefully has appeared, then I really don't see the harm.
IMHO, "Good answers would be too long for this format" seems inapplicable here on Cognitive Sciences. On other SE sites, sure, but the character limits here aren't bad (30,000 per answer). I managed to hit the limit myself on my first version of this answer, but it was a very long, deliberately overzealous answer, and turned out to be too long to comfortably fall within fair usage rights for legal purposes. If you take a glance, you can get an idea of just how much effort it takes to become literally too long for this format. Bear in mind that a great number of the characters in this answer were used up with code and hyperlinks, so a pure text answer could've been much longer still.
I have very little sympathy for readers who opine, "TL;DR" on matters of cognitive psychology. Scientific journal articles (let alone books) are far longer than our answers here; my dissertation exceeds the character limit by almost 400%. This is why we skim at least a little bit unless we're deeply interested in every detail and nuance. My instructors have had limited sympathy for the amount I can reasonably expect to read, so I've gotten pretty good at skimming. I skim practically every answer I "read" here, and highly recommend it. Therefore, what kind of answer would be too long for this format is a separate question in my opinion. I can't think of a clear question of empirically-based cognitive science that couldn't be answered well in far less than 30,000 characters.
Despite the implications of this paragraph, I think good answers will tend to be succinct in general, or at least provide a succinct summary, even to incredibly broad questions like, "What is consciousness?" This is the intrinsic nature and challenge of work in our field. Hence I do not believe even this question is too broad. Wikipedia's intro on the topic is less than 10% of the character limit, and it's quite a good answer to such a question, which is more problematic for lack of evidence of original research. If we feel the need to close questions for lack of original research, I do not think we should do so by voting to close as "too broad"; this would be misleading.
"Adding details to narrow the answer set or isolate an issue that can be answered in a few paragraphs" is good advice, and may be the most usefully clear content in the "too broad" banner text. I don't think we need to close questions to provide this advice, and I'm disinclined to enforce it as a rule, not just advice. Still, in the truly excessive cases described above, I can see and respect reason for disagreement, and am of course willing to participate supportively in the democratic process. In some of these cases, I too would vote to close as too broad...but in most cases, I will probably find other reasons to close more useful.
This is not to say "too broad" is useless – again, for example, it is the best way to close a question requesting an excessively broad reference list that comes to my mind. I am only saying that "too broad" is probably the least appropriate reason to close most problematic questions here. Most broad questions about cognitive psychology are manageable nonetheless. Exceptions will be rare by my standards. If this seems unreasonable or unclear, please comment. I would be happy to consider any examples we have of questions closed as too broad.
For instance, I agree that @what's example of the NLP question is too broad, but not for its length. It is somewhat unclear for its length and lack of attention-organizing formatting, so I can understand the downvotes (I might not downvote it myself...but I wouldn't upvote it), but what makes it too broad are the demands placed on answers. I find it inconsiderate to demand depth, citations, and analyses, and to rule out focusing on individual aspects. This is the problem I referred to above: explicitly demanding a complete answer or more answers than people can be expected to provide. (For free!) Ain't nobody got time for that.
[Edit]: Found another good example of a question that even I think is simply too broad as is: https://cogsci.stackexchange.com/q/5902/4086
As men prove their instability on history, what would happen if all men on the earth die? Would the remaining women continue violence/war accross the world? Are women as dangerous as men when they have power? Please take diverse effects of ovulation into account.
The problem of explicitly requesting incorporation of a broad field of related(?) info occurs again in the last sentence, but the unique problem is the speculativity of the first two questions. Of course, mixing them with the third doesn't help, but IMHO, the third question is manageable (if lacking evidence of initial research effort). In some sense, so are the first two questions – I don't think answers would necessarily, inevitably be opinion-based – but "what would happen" in an apocalyptic scenario is an unclear question, and would probably remain too broad even if that weren't the case. I don't especially mind limited speculation of the sort the second question requests, but I think the first one at least needs to be reworded more specifically and as a premise rather than a question.