I recently downvoted an answer on SO because I believe it didn't actually answer the question, and before I could add a comment, the answer had been deleted. Two minutes later, I looked at the question again, and the same user had re-posted his answer, without the downvote.
I've seen this guy remove answers with negative feedback/downvotes in the past and repost them exactly as they were. My biggest concern is that by getting round the system this way will hide legitimate feedback that may be very relevant to whoever asked the original question.
I feel there's an argument for requiring a vote to close ANY answer or question with any kind of feedback. Personally, I've only ever deleted one question that had answers, because I realised there wasn't an easy way to explain what I was asking, and realised shortly after I posted it that it wasn't possible anyway.