They leave it there because of automatic updates, then you can look and see what apps have been updated and what the update was about (click on "What's New"). When you do manual updates you have a chance to check it out before updating. So, that is the reasoning for it. Otherwise you would not know what apps were updated and, if you something worked differently, you wouldn't know why, this way you can come back to this.
At this time (iOS 7.0), update on your iOS device manually or automatically, they seem to stay there for two weeks, then disappear. There are no known settings to change this, no known ways to delete them. At least the number flag goes away. (There were threads on this during the betas.)
If you wire into your computer and sync via iTunes, the updates will not show here.