I agree that music identification questions are frequently uninteresting, of limited use to future readers, and have some superficial commonalities with [identification-request] questions, such as the "hit-and-run" nature of the users asking these questions. However, these are what I might call "pragmatic" issues. If the only problems with [identification-request] questions were "pragmatic" ones, I'm not sure we would've ended up banning them.
Indeed, the chief problem with [identification-request] questions (as I see it) is that they were "philosophically" unsound, if you will. In particular:
- While a community of anime & manga experts are probably the people best-suited to answer identification requests about anime & manga, the kind of expertise involved in doing so is somewhat orthogonal to the kind of expertise needed to answer all of our other questions. In practice, it turned out that, with the exception of a small number of exceptionally well-read users, these questions were answered primarily by means of adept googling. Search engine wizardry is not really the "core mission" of our site, so to speak.
- They frequently had more than one "correct" answer, in the sense that there were multiple different things that fit the description provided in the question. While the ability to have multiple answers is a feature of Stack Exchange, in this particular case, it moves the question into the realm of an out-of-universe list question, which we strongly proscribe for other reasons.
- They sometimes were not about anime & manga at all, and we had no a priori way of detecting this.
Music identification questions anchored in a particular show or franchise suffer from none of these "philosophical" problems, and so I see no problem keeping them around. Every Stack Exchange site has its long tail of mundane "workhorse" questions; music identification questions are shaping up to be ours, and I don't think there's anything wrong with that.
[W]hat are they contributing to our site?
This kind of information is usually not easily found elsewhere on the internet (which is, I think, part of why we're starting to get so many of these as our site grows). As such, I think one way to look at it is that the users asking these questions are helping us to contribute to the broader internet anime community by turning us into a repository for this kind of information.
(Personally, I also happen to enjoy answering these questions for shows whose music I like. I assume there are some other users that do too. So in that sense, these questions contribute by virtue of providing more content to keep users like me interested.)