Before I finally deleted my Twitter account I had considered going down this route; it makes some degree of sense considering the real time nature of the service but conflicts with the notion that tweets can also serve as a public record.
I guess a lot of it depends on who you are and how attached you are to what you've posted.
It makes me wonder whether taking the same approach would work with blogging. If truly "blogging for now" then maybe, but it would remove the element of talking to my future self which is a big part of what I do.
It's an interesting idea, though.