Both, but have a time limit on editing or have a "edited" box underneath like with someone asking a question updating it. And if people say it might cause trolls, well mod powers on plenty of other sites allow you to see if someones edited/deleted and what the original content was.
I mean, I would like it overall, but I know why it isn't a feature. Trolls would use it to their advantage to try to bypass site rules. They could say something offensive and then change it quickly, pretending they said something completely different.
I would like it but do understand why it is not allowed - Say you made a safe question and got 10 people strongly agreeing with it then (being a troll) changed your question to make it horribly controversial, the ten comments that strongly agree will still be there on a horrible statement.