I'm glad Twitter doesn't keep a record of my tweets. Perhaps for what you want, they could make it an opt-in service, but for invasion of my privacy, I'd just as soon not. And for their service load (media needed to store your tweets and server bandwidth time needed to make them accessible to you) I can well see how it might be a payable service.
Who said Twitter DOESN'T keep a record of your tweets? What's been said is that Twitter doesn't let users access any archive of your tweets they may well have, and that they may well continue to mine. Your point makes me want to revisit the standard terms under which users license their original tweets to Twitter.
