Identification requests are the bane of my existence over on Anime.SE. They suck for a billion reasons. If anything kills Anime.SE, it's going to be the identification requests.
That said, I don't know what shape mythological identification requests would typically take, and it is not completely inconceivable that they could potentially maybe somehow be sufficiently non-terrible as to warrant their being permitted on this site.
As such, I suggest that we wait for a small number of identification questions to arise organically, and then look at them with an incredibly critical eye. If, somehow, they turn out to work reasonably well for this site, then we may as well permit them. But in the likely event that they do not, we ought to do away with them with extreme prejudice.
I should add that I do not view "in which text is the story of X told" as an "identification request". These questions are objectively answerable and are useful to future viewers, and I think are well-described as "reference requests".
My objection to identification requests here is to questions of the form "I remember A, B, and C happening in a story I read when I was little, but I no longer remember any of the proper nouns in it! What story could it have been?". These are unlikely to be useful to future viewers and require answerers to read the mind of the question-asker.
"Here's a picture of something mythological. What is it?"
I think this is again a separate thing from the memory-based identification requests I object to. For example, if someone posts a photograph of a relief from the Parthenon and asks which deity is depicted, I think that's an okay question. Questions about the iconography surrounding various mythoi seems like a thing this site is well-suited to answer, and are not all that different from other questions about mythology-related art, such as "Why is X displayed battling Y on this vase?" or "Why is Q always depicted with a widget in his left hand in sculpture?".
What I fear is that we're going to get people doing nonsensical things like taking clips from Clash of the Titans and asking what deities are depicted therein. It is these questions to which I strenuously object.