After giving it some thought, I think the basic principles governing the discussion on context are:
- Determine where the OP stands. Have they tried anything? Are they trying to get their homework done for free? What level of answer will they understand?
- Value for later readers. Is the question of universal interest? Will different viewpoints yield fundamentally different answers? Is the question from some book or other source?
One of the main objections against including OP's work in questions is that it only serves part 1. On the other hand, it is tremendously effective there.
Another point of relevance from a quality perspective is that the length of the question should be minimised while maximal useful context is included. ("No context" is an explicit possibility here.) Additionally, in the light of generality, the amount of context specific to OP's situation ought to be just enough to make answering the question to their needs feasible.
Taking the above into consideration, I propose to start valuing context according to the following hierarchy:
- Meta-context: Why is this question asked? Where does it come from?
- Literature context: Is this a question from a book which you're studying? What are similar results or other relevant links?
- Personal context: What have you tried? Are you taking a course?
- Definitional context: What does $X$ mean in your post?
The reason I put 4. at the bottom is because in the unusual case that it's not obvious, the confusion is easily resolved by one or two comments and a subsequent edit.
As for 1. and 2., I think they're the most important types of context, because nobody can supply them but OP while they are important for both of the context considerations mentioned at the top. Moreover, I contend that when these two types of context are present, the added value of someone's work is limited.
I think the schema outlined above goes some way to optimise for pearls. For questions of intrinsic interest, one or two lines addressing the first one or two points would usually suffice. (e.g. "I found result $X$ in book $Y$, which made me think of $X'$.")
As the percentage of information only applicable to the situation of the OP (aka "work") increases, I conjecture the average number of votes, views, and answers to go down, in accord with the reduced usefulness of future viewers. I guess the discussion on how to deal with the ever-growing lake of past questions of this type is something for another thread. The same goes for the fate of proof-verification questions.
TL;DR I think we ought to migrate from "what have you tried" to "why are you asking this and where does it come from". This should at least take the burden off of the posts with intrinsic interest.