Twitter is giving up on encrypting direct messages... March 2014
...At least for now.
This shows how unnecessary encrypting is sometimes. Some people like to encrypt and encrypt everything, and don't consider a solution "usable" if it not fully protected.
I'd argue that twitter has always been a very "public" and "exhibitionist" kind of websites where the private messages have never been a core feature (and it's actually not a really well done message system) and no user is obviously going to use it for "serious" matters. So why spend time encrypting it ?