Probably the original idea behind twitter was that people share random things that are relevant to the current moment only (or not relevant at all). And it is still a predominant use-case, but there are others. People generate funny phrases, share great videos and links that they just found. Things that will be relevant in a month and even in a year.
Unfortunately, twitter makes it really hard to get back to your old tweets. It stores only the latest 3200, but to get to the 3200th tweet from the UI you need to be persistent – there is no paging, and search just doesn’t work like that, even if you know parts of your tweet.
Having 10000 tweets, I realized my first tweets are gone. Forever. The service I used to make backups was abandoned and the data – deleted. And that’s not good. My tweets are my short thoughts, my micro blogposts. (Does wordpress delete older entries?) I don’t think it will be that expensive to store everything forever. Facebook does. Making it accessible is a bit trickier, but the user is likely to wait more if he tries to access something old, so the performance doesn’t need to be as good as with new tweets.
Perhaps twitter wants to be exclusively about what’s happening “now”, and never care about last week, but that’s not everyone’s use-case. Having created a horizontal product means you have to support horizontal use-cases. Pinterest seems like a better match for just one of these use-cases – interesting things you find on the Internet, but do I need yet another service just for that?