Just because you don't see a useful or 'good use' of it, doesn't mean that others won't. If you're just randomly looking at tweets, you're going to have a hard time finding anything useful. But if you do a targeted search or data mine, then you can come up with useful stuff. Say for instance, all the tweets somebody has made since the time they went online. You can get a pretty good idea of that individual's development. Or the tweets on a day like 9/11.
And like others have mentioned, it's not like resources are scarce to archive them. 140 characters could hold literally trillions upon trillions of tweets on a single hard disk.