I think it's less about people using streams more (though I think that is true) and more a representation of what is happening to information.
In the document (or batch) mode of interaction, you have full knowledge of some set of content. In stream mode, you only know what's happening right now in the stream and what has happened in the past. You don't know what you don't know. Traditional web form submission seems very document/batch oriented. The RIAs being developed are more stream like.
I think there are some fundamental information concepts going on here. We've been treating information like it's a static set, but in reality it's more like a continuous movement of data. At any split second in time, there may be a static representation for some information. It's almost as though every transaction in a relational database is like a single frame in a 3D game. I think this will get more and more stream like and continuous as our systems develop with greater distributed concepts like the semantic web.