Problems with this type of question
The StackExchange guidelines are in fact not to allow these types of questions at all, for several of the reasons you've described, summarised in the following statement:
After a year I am convinced that guessing game questions do not meet our goal of making the Internet better.
Quite the opposite, in fact.
Here are some of the key points from that article, though I recommend reading the whole thing. (Remember, this article is talking about these questions across the whole of StackExchange. I'll get on to whether I think these objections are relevant to ELU specifically after I've summarised what the SE blog has to say about them in general. So please read further down before jumping in with another "Omg it doesn't apply!" comment.)
- Guessing game questions tend to be vague, badly researched and do not tend to fit the "practical, answerable question" criterion of the StackExchange question guidelines.
- Guessing game questions are not helpful for future viewers. A future questioner with the same question is unlikely to be able to search and find the original nebulous question.
- Guessing game questions set a precedent for "do my work for me" questions.
- An expert in the topic should be able to have at least some confidence that the answer he’s writing answers the question. This is not possible with guessing game questions.
- Guessing game questions aren’t educational, because there’s no way to learn about the process of discovery.
I don't think the last two apply to ELU as much as to the other sites with "guessing questions", but I do think we have some extra concerns.
- Guessing game questions can get ridiculously localised when you are asking for a specific word that may or may not exist.
Assuming we're not going to abolish word/phrase requests any time soon, we need to address these concerns.
Ways we might be able to make it work on ELU
Guessing game questions aren't "practical, answerable questions"
They can be, but often they're not. We need to be strict about closing those that aren't, to firmly encourage the idea that you can only ask these types of question if you define your scope extremely well.
Answerers cannot be certain that the answer they are writing answers the question.
This is less of a problem here than on other SE sites, because there is a key difference in that questions tagged with things like "story identification" or "identify this game" have a correct answer in mind which you have to try and guess. If you find a book that fits all the criteria the questioner asked for but it's not the book they're thinking of, that's no good.
single-word-requests or phrase-requests on the other hand are looking for any word that fits the given criteria. The questioner doesn't necessarily have a single correct answer in their head.
We can further help by making sure the answers are well explained and describe how the word or phrase fits the request.
Guessing game questions aren’t educational, because there’s no way to learn about the process of discovery.
This is also less of a problem here. As long as answers are well explained and discuss similarities and differences between the hypothetical requested word and the suggested word or phrase, they can indeed be educational.
Ways we will struggle to make it work on ELU
Guessing game questions are not helpful for others who have the same problem in the future.
"A future questioner with the same question is unlikely to be able to search and find the original nebulous question." We can't do anything about this one. It's the very nature of the question.
Guessing game questions set a precedent for "do my work for me" questions.
The broken window analogy. We can attempt to crack down on this by being very strict with the word requests that we do allow. However, this may not be enough.
Guessing game questions can get ridiculously localised when you are asking for a specific word that may or may not exist.
This is quite hard to address. I'm not sure what to suggest.