Site Upgrade Discussion, Q&A, FAQ

It's a little counter-intuitive, but 'deleting' a conversation happens when all participants have clicked the 'Leave Conversation' button. There's no storage limit on conversations, so the need to delete them isn't quite as strong.

 

I've got good help, is all

 

No, the software developers didn't consider it necessary. The draft is only saved for 24 hours, so it'll delete itself if you decide not to post it. The draft doesn't get in the way of posting elsewhere on the site, as it's only temporarily stored in the specific thread you composed it in.
I appreciate their philosophy... no reason to waste space on an unnecessary button, especially a button that can cause so much frustration when accidentally clicked.