I kind of doubt that it's a caching issue. Twitter feels a lot like email to me -- sending a tweet is a lot like emailing to a group of followers. (Though it's unlikely they implement it that way because of the number of tweets that go unread.) Email providers operate at a scale similar to Twitter and don't replace your email with popular emails to increase cache hits.

Maybe to improve profitability you'd want to improve how much you can serve out of memory, but I think Twitter has more than enough compute to just generate your page for you when you visit. (I haven't seen a fail whale for over a decade!)