I wonder how cheaper would it be if tweets were removed in, let's say, six months.
That said, I thought about this recently when @pmarca took a break from twitter and all of his tweets disappeared, and I figured, "Well, yes, I follow him and enjoy his tweets...but I never planned to go back and read the old ones." It is a fleeting and temporary medium, like a conversation rather than an article or book.
Nonetheless, I really doubt storage is anywhere near the majority of the cost of running Twitter. It takes a lot of 140 character tweets to fill up a terabyte.
Tweets contain photos, videos, gifs, etc. Text is far from the only things that would need to be stored.