I agree with Robert. These just don't seem like a good fit here.
In my opinion, group writing exercises should be a way to learn and improve, and I don't think they can be very effective at that within the stack exchange framework.
There is no correct answer
I don't even know what the check mark would mean in this context. I guess it would denote which "answer" the original poster liked the best. However, this makes it feel less like a constructive exercise and more like a contest.
Voting is corrupted
Corrupted is probably too strong of a word, but voting is definitely being used differently in these questions than in most others. People are going to vote up the entries they like ("good" writing) and vote down the entries they don't like ("bad" writing).
Upvotes are typically supposed to show that you've contributed to the good of the site (with a good question or answer). However, the value of these writing exercises is primarily in the criticism! An answer might be downvoted for poor writing, even if it ends up being a useful example. Similarly, a very well written piece might be heavily upvoted, even though it garners few comments or useful criticism. Votes might actually go against the most useful content.
Community wiki removes the reputation gain associated with these votes, but that is a pain too - as the site gets big and there are a lot of these questions, it's going to suck for the moderators who have to change them all to community wiki.
Also, I think this continues to add to the contest feel and detracts from the constructive criticism.
Comments and editing don't work well for this
The length limit on comments is a pain, and they get very messy very quickly, especially when it's a dialog of more than two people.
It's also likely that these posts will get revised a number of times, and comments are not linked to specific revisions. An answer with three or four revisions and 15 comments will be difficult for newcomers to follow.