In my circles, there's Weird Twitter for creativity. Political Twitter, which is now a dominant form of medium-length blogging where the punditry is broken up into 140 character paragraphs. Art Twitter sending out all sorts of photos and paintings. Cute Twitter for DogRates and other forms of reporting on fuzzy things. Twitter is still good for breaking news, and for on-the-spot reporting. Even great for weather. I live in a stormy part of the country, and hitting #kswx can be good on bad nights for getting reports from the people around me.
And, of course, it's the premier way for the leader of the free world to spit his thoughts directly at the public.
They may not have found any way to make money, but Twitter is a core part of internet culture. It's like Instagram, Reddit, Tumblr, etc., that it's so big, it can't be pinned down to just one aspect or another.