You're just flat out wrong. That's why there's a tab dedicated to replies. Twitter conversations can be incredibly interesting and benefit all participants by being public. Twitter's setup hugely encourages @ing people in your tweets.
Also, conversations look different when you're looking at them from one of your lists, or if the people you are following are different than the people I follow.
So many clunky issues that you need to be on top of for it to make sense, and this is what's lost on the general person.