This question is predicated on a false premise, namely that we are still getting identification requests because we have strong SEO specifically for questions asking for anime/manga identification. That is a misunderstanding of how SEO works on SE sites.
By far the most crucial aspect of SEO is the presence of tags. Popular tags give keywords which are present on the questions they are tagged. Tagged questions link to the tag pages, which link back to all the questions with the tag. Google looks at the internal structure of the site and determines what the big topics are. For us, until early 2016, identification requests was one of the big topics.
None of that is happening with identification requests, which is ultimately the reason why we removed identification-request in the first place. The tag barely even exists at this point, and there is no risk of it growing (in fact, as time passes it will shrink relative to the site as a whole). Google also updates regularly enough that we can't reasonably blame any form of caching. Individual posts in random tags will not have any big effect on SEO just from their titles. Indeed, I tried a few representative searches for things like "What is this anime?" or "Anime identification" and I never saw this site on the first page of results, except this single question once near the bottom of the first page of one search: Where is this picture from? How do I use Reverse Image Search to find the source of an anime/manga image?. If you want to propose doing something specific with that question, such as locking or deleting it, I think that deserves a separate meta post, as it isn't really an identification question at all.
So if we aren't optimized specifically for identification questions, why do they keep showing up? The answer is simpler than you think. It's because that's still a common type question people on the internet as a whole want to ask about anime/manga. We're no longer targeting identification questions specifically, but we are still targeting people who want to ask questions about anime/manga generally. And a lot of those questions are identification questions. Like it or not, that fact should be obvious to anyone who was on the site when they were allowed. Even if we remove every reference to identification questions from the site, the rate of incoming identification questions might drop 10%, but it would not drop to 0. Even in the early days of the site, when we had barely any external traffic, identification questions occasionally showed up, and not because of any SEO-related phenomena (the tag then, as now, was not one of the top ones); they will continue to appear occasionally as long as this site exists and regardless of anything we try to do to preempt them.
So what can we do? We could try to kill all SEO for anime/manga questions in general. Which would basically amount to deleting the site, as far as search engines are concerned. Obviously we aren't ever going to seriously consider this, but it's the only way to completely eliminate incoming identification questions.
We could remove identification-request from the 27 remaining questions that use it. However I suspect at this point the tag (which is not even in the top 50 tags on the tag page) is doing more good than harm, by announcing that identification questions are no longer permitted and giving an error message when users try to use this. I suspect this is why, concurrent to the overall drop-off in identification questions, we have seen them become low quality spammy questions: the askers who wanted to ask serious high quality identification questions and put work into asking well tend to see this and withhold their questions, leaving only the ones who are not willing to put much effort in. Almost anything we do to reach them and preempt them from asking is likely to be in vain for that reason.
We could change the titles of the remaining identification questions to be less obviously identification-related. Like I said above, I suspect this would only affect things at the 10% level or so, not completely eliminating the remaining trickle of identification questions. I'd be open to suggestions in this direction, but personally I don't understand the details of SEO enough to know what kinds of changes would affect the situation, and it seems equally possible to make the situation better or worse with a move like this, so I don't think it makes much sense.
Or we can keep doing what we're doing. It's not a big deal at all that occasionally someone asks a question that we don't take and we have to click a few buttons to close it and remove it. The questions are removed quickly and there's no lingering effect, so basically no harm done to the site. Unless you spend a lot of time in the chat room or review queues, you'd never even see 90% of them. It's by far the easiest moderation we ever have to do on the site. If annoyance over needing to moderate identification questions is the main motivation here, the only way way we ever could have avoided that was to not ban the questions (or even restrict them); deciding to ban identification requests was exactly a decision to moderate the new ones that show up. The community decided that the effect the questions were having was worth the extra sustained moderation effort to remove them, and so we just have to keep removing them.
Of course, we also should not forget the negative effects of removing hundreds of well-written, answered questions from the site as well. Some of the information in the identification requests we've closed is not available in any form anywhere else. Some of it is linked to from this site or externally and some have thousands or even tens of thousands of views. Most of the questions that remain are well written and solidly answered (contrasted to the reason we banned the type of question, because a lot of them were poorly written and fundamentally unanswerable). The fact that we no longer accept more questions of this type does not mean that we should destroy good content that they contributed when it was allowed, nor is it a license to ignore that content.
Additionally, removing such posts would delete most of the tags that were newly created based on the resolution of the previous request, harming the overall accessibility of the site (and wasting many hours of senshin's time). Based on this query that's over 200 tags, which is quite a large number, over 10% of all the tags on the site if I counted correctly. In my mind, accessibility is one of our greatest issues, especially as SE has provided next-to no technical support to make it easy for new users on sites like ours to ask questions that may not yet have appropriate tags despite acknowledging this problem years ago. Deleting all those tags again just because we still have a (completely expected and predictable) incoming trickle of identification questions seems like a huge overreaction.
When identification were allowed, many people were working very hard to improve those questions and answer them, and the ones that are still around (and historically locked) represent the best of that effort. Now that they're disallowed, I think having to click 4 or 5 times, taking 10-20 seconds apiece, to close vote such a question a couple times a week (reading the question is barely even required, and the close notice is clear enough that commenting isn't necessary) doesn't even register as a real problem, and certainly not one that we ought to be removing hundreds of old posts over.
In any case, if the real worry is that a sizable fraction of the incoming questions are identification questions, I think it is ultimately more productive to ask what we can do to improve the existing allowed questions and attract more questions (including asking more ourselves). The overall quality of the site as a reference has nothing to do with what fraction of incoming questions get deleted immediately; it has to do with the quality and quantity of good questions and answers that stick around. We should think more about what we can do to increase those numbers (especially since the raw question/day numbers have dropped dramatically due to the removal of identification requests as well as some very popular series ending) and less about the occasional bad questions that take 10 seconds to deal with.