I don't think the question as to the appropriateness of cryptic crossword clues can be resolved with reference only to four recent examples.
Cryptic crossword clues are not all the same. The best setters put a lot of effort into developing different kinds of clue, and SE could be a marvellous resource for people doing exactly that.
Writing cryptic crossword clues is a respected art, doing it well takes great skill, and as with any art there is a lot of scope for originality. (@Gilles, you sound as though you're not into it - which is fine but no reason to knock it.) Good clues are neither trivial nor easy to write. Certainly you can get clues that are of low quality, but I don't think anyone is arguing that SE should be a repository for low-quality anything.
Crosswords are a genre of puzzle that a lot of people, including people who are already very skilled at solving or setting, want to get better at solving, setting or both. Ideal for SE, is what I'd say.