You have choice to have either option but for quality and management I agree with your views as members shouldn't delete posts and can edit until certain time so it maintain the forum structure otherwise it will create problems.
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One thing that I really like about Bizdustry is that they allow members to edit and delete their posts, provided that they have a legitimate reason. Other forums do not do this, and this gives credence to your assertion.I have been in some forums that never allow members the privilege to delete their posts for any reason whatsoever. The members are only allowed to edit their posts for 15 minutes after they are made and after that, they can't edit it again but only report it for a moderator to attend to it. While some forums allows members to delete their posts whenever they want which is something that's not good for the forum in my opinion.
I think it depends on the forum you run. I think it's fine to allow people to edit their posts in most subjects, but if it's a serious topic like a debate, I think I'd make it where you can't edit a post for too long after, maybe 15 min like someone said or maybe even 30 min. I think giving them some time to be able to edit their posts is fine. And as long as it shows it was previously edited, that is a good thing too, it at least shows something was changed.
What I don't like is when forums allow you to edit, but it doesn't say when a user edited it.