Thanks to @Hakase and @Madara for answering my questions about how this would be implemented. Since I haven't totally made up my mind on the specific issue of using the phrase blacklist, I'll summarize the pros and cons as I see them.
I'm still wishy-washy on the subject, but I'm leaning towards supporting the end of id requests altogether. @senshin summarized the response to this proposal from that point of view in a comment:
Ah, yes, let's put more lipstick on the pig.
Movies and TV apparently has also gotten sick of id requests; when they had the initial discussion about whether to allow them, Robert Cartaino posted an answer saying they would regret it. On January 6th of 2015, Movies and TV moderator Napoleon Wilson posted this comment on the answer:
Oh my, how right you were with all of this, if we just had listened to
you back then.
Arqade has apparently decided to ban id requests on their site.
Using the phrase blacklist would just be a very small solution to a very small part of the rather large problem of lousy id requests. On the other hand, there seems to be widespread disagreement among the community on whether allowing id requests is a net positive or not. I can certainly see some negative aspects to getting rid of them, but it seems like when you need a custom close reason that only applies to one specific tag, that tag is a problem.
Coming at this from the other side, we already get complaints that we're unfriendly to new users. Imagine being a new user, possibly with subpar English skills; coming to post an id request; writing "when I was 10" in your question; and having the system itself pop up a message complaining about how bad your question is. It's like those password checkers that reject all your passwords—"this one doesn't have any uppercase letters", "this one doesn't have any special characters", "this one is too short", "this one is too long", "this one only has 25 bits of entropy, which according to information theoretic principles implies it can be cracked by a determined attacker in 3.23144153 minutes"...this site is supposed to be fun. Personally, I think we can do without a lot of these users posting id requests, but this could be annoying even to users who approach in good faith, read the FAQs and the tour, and do their best to post a good question.
I also still have some concerns that the system is too coarse-grained. If we're just doing a simple regex search, I'm not sure we can avoid false positives effectively enough to make sure this feature stays out of the way for most users and only affects users who really are writing an awful, vague id request. I think a lot of what Paul Graham writes in the first section of his essay on spam filtering is applicable here: using a regex-based filter like this is similar to using a spam filter that looks for "DEAR FRIEND!!!!!!!" in the subject line. It's us trying to identify what we think are the relevant features of bad id requests. Users who are really determined will find new and wonderful ways to be totally vague and unhelpful, while users who are actually trying may just be disgusted and put off that they're being called out for using a common English phrase. Some of them may find their way to meta to find out what they can do about this, but many more will probably just go "Jerks" and go off to some other anime site. Like I said, I don't know how much we really need these users, but it's something to consider.
On the other hand...jeez, every fricking person who writes an id request uses exactly the same vague, totally unhelpful wording, as if we know how old they are and thus what year it was when they were ten! Maybe it has something to do with the fact that user profiles used to display your age; maybe they thought people could just click over to their profiles and do the calculations. It's clearly not a good use of anyone's time, especially our moderators', to go through every single id request and post a comment saying "Can you please give an exact year? We don't know when you were 10, you see, as we don't know you, and can't even guess how old you are since you've put a picture of an anime character as your avatar."
Maybe we could try doing a test run. Set up the filter and have it on for a few months. After a few months, come back and look at the crop of id requests posted in that timeframe to see if there was any improvement, however marginal, using a set of statistics like the ones in JNat's meta post. After all, if we have the filter in place, then many of the people using this phrase will likely either write better questions, or give up and go away. Whatever happens, we can use the statistics to find out what effect the filter is having and talk about whether we can live with that.