Twitter had the problem, that when you tweeted a post accidentally twice, it showed also up in the timeline twice. That was a little bit nerving, but you always have the possibility to delete your published tweets. This will disappear in the timeline.
Another side effect of deletion is, that this single tweet is no more secret and may be too late. Hopefully it was not re-tweeted by someone before your deletion.
Another good reason for the duplicate re-tweet checking change on the Twitter API is to prevent spamming. Let’s say a new user is created and writes a script tweeting nerving stuff multiple times. This will be detected and disabled.
This way of clean up may also help to keep the database a bit smaller.