An interesting idea, but you would have to make it where the first post in a thread could not have replies barred. Otherwise, we would have 'threads' where we could not post.
I also think this idea is a little abusable, and potentially annoying.
As for the main idea. I like it. When we first got the 'edit' feature I assumed that we would also get a delete feature. No such luck.
The reason is, I assume, that a member may be in the middle of writing a reply when you make your edit. In that case, they reply to the altered post. The problem starts when we think about deleting a post that someone is trying to reply to. Suppose I spend 15 minutes writing a reply, then, guess what?, there is no such post. At best the post can't be posted, maybe it's lost. I'm not sure what would happen, but it would be aggravating. Now that I think of it, it surely has happened when an admin deleted a post, so someone knows.
Either way,
It may be that we do not have a delete button because it would be,
A. difficult to instate and/or
B. easily abused and annoying.
Which isn't to say I don't want one, I do, but I'm not convinced that it's worth it.