Honestly, my brain isn't wired for twitter. There's so much info coming at me from so many different people that I can't remember who sent what. I'd have to take notes to keep up with everything. As a matter of courtesy, I like to be able to tell one person from another. Constantly confusing people shows a lack of appreciation for them as individuals.
Also, I'm tough on portable electronic devices, so I usually leave them in a safe place whenever I'm busy with something which takes away from the immediacy of something like twitter or texting. I'm one of those "on task" people-I concentrate on the task at hand, so that I can finish up and go on to other things like leisurely communicating with people when I can give them the full attention that they deserve. It's just a different style, neither better nor worse than the multitasking thing.