My viewpoint is that many of the identification-request questions coming in are bad questions, but few of them need to be closed. This is, in my opinion, the same viewpoint that JNat suggested in his answer here.
Hence, IMO the first course of business should be to create an FAQ on meta regarding how to ask (and possibly answer) ID request questions well. This should be linked to in the help center and the tag wiki of identification-request. The guide should include all the common problems we observe with ID requests and what the best way is to write them. The point of this is that many users will not know what sort of information is useful and what is not, and the FAQ will help them discern that. If there is interest in this I am willing to write a first draft, but it should be a community effort. Once this is in place, any new ID requests which are clearly low-quality should be directed to this with a request to improve the content along the lines of those suggestions to give them the opportunity to improve.
If the suggestions are not implemented and the question continues to have some of these problems (as will unfortunately occur frequently no matter what), the question should be downvoted. Note that negatively voted questions without answers will be deleted eventually which means these will not be a sore thumb forever even if we don't close them. Furthermore, questions at -4 or lower won't show up on the main page. If a question is downvoted, it's clear that we don't see it as good content, so even if it sticks around it isn't as much of a broken window. Downvotes are supposed to be the primary form of quality control on SE sites, while close votes are reserved for questions that will not work in this format and flags for content that needs immediate attention. Thus, I think they are the right tool for dealing with most of this.
As for which questions should be closed, I think the existing close reasons are satisfactory once we interpret them properly. The ones that are most significant are unclear what you're asking and too broad; the other close reasons rarely apply and it's clear when they do.
An identification question is unclear if it doesn't even approach reasonable English, and is incomprehensible. This is pretty obvious, but it seems to be more common for identification questions than other questions. Here's an example question that should be closed as unclear.
What anime is this?
- Blue hair
- Uses mecha
- Lots of girls
- Like Code Geass
I have no idea what that means, and neither would anyone else. You could guess what it means, but we're already playing one guessing game by accepting ID requests, and we don't need to have guessing games inside our guessing games. If you see a post with a comparable level of incomprehensibility, close it as unclear what you're asking. A comment asking the OP to clarify is also in order (and if they do the question should be reopened).
A question is too broad when it admits many possible answers that can not be objectively distinguished in terms of quality or relevance in any way. In the context of ID questions, I propose that any identification question which is satisfied by at least 2 unrelated anime/manga is too broad. The reasoning here is that if there are two anime with those characteristics, in all likelihood there are at least a dozen. In the rare cases where there are 2 cases but they're easily distinguished and there are no others, you may be able to fix the question by asking for clarification, but 90% of the time questions with this level of detail are just too general.
To make this explicit, if you can think of 2 separate anime which satisfy the criteria required and you think there are more, you should vote to close the question as too broad. You should also leave a comment to the effect of "There are many anime which satisfy this description, such as example 1 and example 2. Unless you can give more information we're not going to be able to definitively answer this. You might also want to look at this guide to see how you can improve your question" This will alert the OP that they need to improve and alert other close voters that the question really is too broad if they could not think of these examples themselves.
I'll give 2 examples to see how this can actually be a bit counterintuitive if you view close votes as a form of quality control.
Looking for anime with a female ninja
I'm looking for an anime which I saw in an AMV. I can't find the AMV anymore but I watched it about a year ago. The anime had a female ninja as one of the main characters (at least a recurring character since the AMV had a lot of scenes with her). I think her hair was either blue or purple. It seemed to be a comedy anime by some of the scenes, and I didn't see a lot of action. Based on the art style it was probably made around or after 2000. Sorry, but that is all I can remember. Can you tell me what this anime is?
This question actually has the makings of a good question, but the OP's specifications just aren't unique enough to make it answerable. If they had asked about something a bit less generic we could have a chance at answering it, but right now the only possibility is that everyone posts their own guess which may or may not be correct. The OP has also gone through the motions of telling us about the location they saw it and the art style; unfortunately these don't help.
In fact, there are many which fit this bill: 2x2 Shinobuden, Himawari!, Kage Kara Mamoru!, Kill Me Baby!, Gintama, .... If you admit the possibility that one or more of the points in the description was slightly misremembered (e.g. hair color) then you have to admit more series as well like Senran Kagura, Juubei-chan, and Keroro Gunsou, and if Samurai characters are also allowed (which would be a common mistake) then the number at least doubles. These are just the examples I could come up with off the top of my head; others may be able to think of more.
In this case, the OP put some effort into the question, but it's just not answerable. We should close it to keep it from getting out of hand with lots of answers (all of which match the description), but I don't think there's any need to downvote. Downvotes are a signal that "you should put more effort into this", while closing means "this isn't going to work here." The two are not automatically related. In this case, more effort isn't possible. The OP has told us everything he remembers, but we just can't help. The best thing to do would be to redirect the OP to chat where we can tell them all the series we can come up with.
Here's a contrasting case:
Help me find anime plz
I'm looking for this one anime it had girls who were actually juice cans. Thx
This is clearly a poorly written question, and the OP put very little effort into it. However, as far as I know, it only matches one anime: Akikan!. So this isn't too broad; in fact it is an answerable question (assuming there are no other anime with girls who were actually juice cans). In this case, you'd be very justified downvoting the question (and commenting to link them to the aforementioned proposed FAQ) but the question does not need to be closed because we can answer it fairly definitively.
You will notice that I've said nothing about descriptions which don't seem to match any series. In these cases, assuming the OP hasn't made a mistake, they aren't solely to blame for us not being able to answer. Not that we'll be able to answer every question even if we try, but we shouldn't penalize the OP for the fact that we don't know the anime they're referencing.
In these cases, you should comment requesting more information if you think it would be helpful to others. If the question is written in a way that you're sure you would remember the series if you had seen it, it's probably a good question that you just don't know the answer to (which happens to all of us). Some examples of questions like this for me are https://anime.stackexchange.com/questions/6396/what-is-this-80s-anime-involving-three-differently-sized-robots-that-can-combine and Manga involving indirect kiss through icecream. The right course of action for these questions is to ignore them or possibly upvote them.
If the data included seems incomplete and you think that you would have trouble remembering the series even if you had watched it (e.g. the only information included was about a side-story or minor character) then you may want to ask for more info. A question that was like that for me is https://anime.stackexchange.com/questions/5802/looking-for-a-manga-with-the-quote-whisper-sincerely-the-words, since it's not clear to me how significant that quote is. (In this case the OP provided all the info they could after such a request was made, though it was in a comment.)
I don't believe that either of the above cases justifies closing the question. Voting is of course up to the individual and downvotes may be justified, but closing the question because we can't think of anything seems unfair considering we wouldn't close even the hardest non-ID questions about the most obscure series unless they had other problems.
Downvoting bad questions more will clean up the bad questions eventually, but it's reasonable to ask if there's anything we can do sooner to deal with these. I don't believe we'll ever be able to get rid of bad ID questions completely. So long as we continue to be a place that accepts ID requests, that is going to be a big part of what people use the site for. It's by far the most common kind of question most people have with regards to anime. They're not the best questions or the ones that will bring in traffic, and in many cases they're really more like low-hanging fruit (which admittedly has its uses e.g. for new members to build up rep answering easy questions), but they do serve a purpose of helping the anime community.
One measure we could take is requiring all users to create an account to ask questions. That already exists on some other sites. This minimal amount of effort will put off the most lazy askers. The other benefit of this is that a lot of unregistered users try to come back later when we ask for clarification. They often have to do so with a different account. We can still tell based on the identicon that it's the same user but they don't have the ability to edit their question or comment on it. That can make these questions a pain to moderate.
However, it'll also put off a small number of people who are asking good questions. I'm not sure if the tradeoff is worth it considering that our biggest problem IMO is that our user base is still very small. Making it tag-specific might help (if this is possible), but people might also cheat and just use a different tag. This is a somewhat serious measure and if we want to consider it further I think a separate discussion is warranted.
We could also impose restrictions on what sorts of questions should be allowed. This is a bit problematic though in that it will always get rid of some questions where the OP has put in effort and just doesn't know the information required. I don't think we should stop people from asking well-written answerable questions simply because they don't know e.g. what decade the anime was from. This sort of meta-data should be recommended in the FAQ, but should not be part of what is required for the question. Unless these questions are literally unanswerable because the information given is too generic or the question is incomprehensible, we should not close them, since that's not what close votes are intended for. Downvoting is fine though if you think the question is low quality and no effort was put into it, which would fit many questions where the OP does not include any sort of meta information about when they watched it or the art style.
Other than that, I don't think we can do anything short of banning this class of questions entirely. If we do that, most of them would just end up on other sites anyway, potentially losing us some good questions and users. In my opinion this is not yet justified. If we write an FAQ, begin downvoting bad ID questions more aggressively, and still find that we're swamped by these low quality ID requests, at that point we should reconsider whether banning these is worthwhile.