Before I begin, I'd like to point out that I think this site does have some great questions about the act of writing, and I really would like to see it succeed.
To me, what really makes Stack Overflow so successful is self-interest. Most expert programmers aren't participating on Stack Overflow aren't doing it so they can do work for free, they're doing it so they can hone their craft. An answered question on Stack Overflow is a mutually beneficial transaction.
I think a problem arises in such a subjective area as writing, because the group of expert artists doesn't intersect as much with expert critics. When a scientist needs his work critiqued, it goes to peer review, and is critiqued by other people who do similar work. As such, a well formed request for critique starts to look like someone looking for free work to an expert editor/critic. Try to imagine what a well formed real-world question where the answer needed to be in the form of original writing and the issue becomes more obvious, for instance:
"I need a tagline for my StackExchange website. So far I've got "Write the Write way! Ask the experts on writers.stackexchange.com!" Is there any way I can improve this? A good line will still be punny, but I feel like I've ruined it by repeating the word "write" too much."
Of course, having written that, it might be a fun sort of question to answer from time to time, but ostensibly it still would look like someone asking for free creative work.
Writing is very personal. Beyond objective changes to fix grammar, (which theoretically belong on english.SE), I don't think there's a lot of room for subjective fixes, as in "Here's your answer with my nifty little literary tricks you may not have been aware of incorporated." The comments on this answer illustrate my point. It isn't something most people are comfortable doing. Of course, since I'm neither an expert writer or critic I may just be wrong about that.
What does everyone else think?