I think they might be too broad, except under certain scenarios.
I am not discussing just this question alone (although it is certainly what made me ask this), but I want to know, in general, what do you guys think about these kinds of questions?
“What type of genre is this book”: close on sight. Debating whether a book is this or that genre is sterile. Many books have elements of one genre, and other elements of another genre.
Subgenre identification is even worse. For example, I've never seen anything good come out of a debate about science fiction vs. fantasy. I mean, Star Wars is clearly fantasy — it's a fairy tale — while Discworld is clearly hard science fiction (it has well-defined physics), but for some reason those works are marketed in different categories, so presumably there are valid arguments in the opposite direction. That's why the Science Fiction & Fantasy site banned and still bans genre identification after sidestepping the issue of having to decide.
Writers has a more nuanced approach, but there the dominant argument in allowing genre classification questions is that this is a site for writers, and genre classification is useful for writers. Writers need to market their books, and marketing a book works differently in different genres. Marketing a book in a particular genre also sets readers' expectation. What matters there is not “what genre is this book?” but “what genre is this book marketed in?” — a rather different question which is not so relevant on a site about literature.
Note that I'm not saying that genres should never be discussed. It's only the request to put a book in a particular box that should be rejected. There are types of questions related to genre classification that are relevant and productive, such as “how are common elements (tropes) of this genre expressed in this work?” (e.g. discussions of Chekhov's gun in a mystery — or rather, a book with mystery elements) or “what influence did this book have on this genre?”.
I agree that such questions are unhelpful. They're taxonomy questions, trying to classify things that don't necessarily fall into neat classes.
Unless they're absolutely trivial ("Is Stuart Little horror, memoir, or children's literature?"), these are questions that don't have an objective answer. Genre is a construct, for convenience and for marketing, but it doesn't really define any hard boundaries. Given that defining what any given genre is, is a hard enough problem, and you can't possibly answer "Is this story Genre X or Genre Y" without definitions of those two genres, questions like these are not really answerable in any sense. At very best, you might be able to reiterate why it could go either way.
Personally, I wouldn't describe all that as "too broad"; the problem isn't scope. "Primarily opinion-based" works comfortably for me -- as in, "there is no meaningful way to categorize it this way or that, besides your own opinion."
In general, this type of question would often be trivial or meaningless, as outlined in other answers. But I'm not so sure that all such questions would be meaningless; at least when the answer would fundamentally affect how to percieve the work:
Neither of these have a clearly right answer, but they are likely to have interesting answers.
Here is another similar question about classification, which has no answer (yet), but does seem interesting enough.