If a place like GameFAQ's, for example, was allowed to edit, the myriad arguments about nothing would probably devolve even further into a grand mess of 'Liar! I never said that!'
But, in a place like this where the moderators seem to be fairly active and the community isn't terribly aggressive, I don't think it'd be a major issue.
There's a solution to that, used by certain forums :
1. When you insert a quote in a reply, you cannot alter the quote in any manner.
(An editing you can unfortunately execute on this forum, which opens the door to modifying a quote to suit one's critical response. I've done it myself !)
2. The person quoted is named, and that information cannot be altered. So, if the quoted person edited or deleted his post, his name, associated with the quote, would signal to everybody that he did in fact say that, previously.
3. I somewhat disagree :
Here, it's the moderators who aren't « terribly aggressive ».
Go read the relatively recent thread concerning the 1.1 update :
It went totally off topic and was full of childish trolling & pseudo-mature countertrolling. No moderator stepped in to put a stop to that « orgy ». (Not that it disturbed me in the least.)
1.1 Preview??