@jwz has also pointed out a different problem with replies/threads - notably that someone can basically hijack your followers to broadcast their crap (whether that's spam, trolling, or outright abuse) to them, and there's nothing you can do to stop it. Their reply will go out to your followers, not just their own.
He thinks - and I agree with him - that the original poster needs to be able to control replies to their posts. Whether that's moderating them, or allowing them to delete obnoxious replies, or something else, I don't know.