The character constraint forces people to say whatever they want to say concisely which I can see as being valuable - it's all too easy to otherwise get lost in the sea of data that is the internet. But that's about it.
How do people use it? Are most people using twitter from their laptop/PC or from cell phones? I can understand the need to keep messages small if you are using a hardware interface that provides a constraint on what you can practically write. But those limitations will go away in time.
I would guess that people will want increasingly higher bandwidth communication, not less. I can see people putting up with SMS type messaging for now, but I'd bet they'll ditch it when they can buy a working star trek communicator.
Seriously, if anyone can provide me with the true enlightenment on this please do so. It sometimes seems as though I'm the only person alive who just doesn't get it.