Summary
The ease of research is easily underestimated and we can produce valuable answers to such questions.
Therefore, we should not have a close reason or general policy to close such questions.
Instead, we can use existing mechanisms to deal with these questions: comment, downvote, and (in extreme cases) close as unclear.
Canned Close Reasons
We can only have three custom close reasons.
Since the proposed close reason would be needed much less frequently than the existing ones (shopping, individual factors, generic off-scope), I would not touch this.
That being said, the canned close reasons exist to ease reviewing and provide more information for askers than the usual comments would.
They do not limit what we can close:
We can close questions for something other than a canned reason, in particular if we agree on this on Meta.
So, for the remainder of my answer I will be addressing the question:
Do we want to close citation-style questions that do not show prior research?
In general, prior research is not a strict requirement for Stack Exchange questions anymore.
Stack Exchange aims to be the thing that you find when you search the Internet for certain questions.
Still, single sites can decide that they do not want certain types of questions without evidence of prior research.
To take the example you mention, on language sites (like English Language & Usage or German Language, which I moderate), the asker has to argue why a dictionary did not help (in most cases).
This is not because we want evidence that the asker consulted a dictionary (they usually have); this is because we cannot give them a helpful answer without knowing why the dictionary did not.
Otherwise we can only create or cite a dictionary entry, which is pointless:
Dictionaries already exist and do a far better job at it than Stack Exchange sites.
Finally note that bad questions that can be answered by a dictionary are a major problem on language sites.
I do not think this translates to questions about applying citation style guides:
It is a real no-brainer to find something in a dictionary, in particular a digital one. Finding something in a style guide is far more difficult. You may still consider it easy, but then you probably know the relevant keywords, etc.
A concise summary or application of a style guide to a specific case makes the Internet a better place as it allows people to get the desired information quicker than otherwise. Replicating a dictionary entry doesn’t.
We are not overrun by citation-style questions, let alone those without prior research. In fact roughly half of the questions you cite at least mention some prior research (though it could be more detailed).
Finally, there is a meta reason to avoid this kind of closure: It will be misunderstood and abused by some close voters (which happens frequently on language sites). For most questions on this site, it does not make sense to require of prior research.
What can we do instead?
Downvote. That a question that could be easily answered by a quick look in the pertinent style guide is a valid reason.
Leave a comment asking the asker to edit their question to elaborate why their research did not help them. Keep in mind and mention that this is to better understand their problem and thus be able to better help them.
In extreme cases, e.g., where the asker already provides a quote from the style guide that appears to answer their question: Close the question as unclear.
