The implementation I've always liked best is that you get X minutes to silently edit posts (or until someone replies, whichever is shorter) for copy editing purposes, but anything you change afterwards gets a little note.
+1 for an edit/delete button. +1 for a like button, or a Thank you button, primarily for authors to signify appreciation for positive comments...or just useful ones...or negative ones, if that's your kink. I don't judge.
That said, gonna go waaaaaay too deep into your comment, completely leaving the topic of the OP's feature request. Bahahahahaha.
Comments don't HAVE replies, which I think leads us to the real problem, one which I believe has been discussed elsewhere: the comment system is not designed for discussions between commenters, it's really only designed for feedback, and it's not great for that either, if you have a substantial amount to say. Concern over edits, and specifically to edits that have already been replied to usually (tell me if I'm wrong about your concern) arises because they allow people to pretend they didn't say something, or that they said something different, after a later poster has already reacted/responded to the original text. That's important for discussions, but the CHYOA comment system is not designed for discussions.
The system COULD be changed to make it a real communications medium, but I assume that would take such a huge revamp it would essentially (or actually) end up a completely different module.
Personally, I would prefer to see better integration between stories and the story feedback forum, where real discussions can actually happen. Or, alternatively, creation of a more full featured (reply, quote, formatting, editing, deleting, etc.) and full sized (so you can write a good, long review without trying to stuff it into a two inch wide comment section that clearly isn't designed for paragraphs of text) comment section for stories (essentially a mini-forum for each story, built into CHYOA's story-side site). I doubt it will happen, though.