It's really painful working with Twitter now. Twitter's display 'requirements' and other aspects of the API are super restrictive after their latest update.
However, the sad truth is that the population of Twitter users isn't going to be shifting anywhere else anytime soon. Most users hardly care about the 'openness' of the platform. I imagine the best way for a competitor to succeed would be by allowing users to cross post statuses to Twitter.. but Twitter API restrictions would kick in there too!
The reason Twitter is popular is because there's a large active community of users and they do a good job of enabling you to discover and follow people you're likely to be interested in. It doesn't really matter how "open" it is, any more than it matters if Facebook or Tumblr are open.
WordPress works with a distributed "install it yourself" model because people use it to power their websites and they want configurability and extensibility. With social networks like Twitter, they want community and baked in support with devices and other services.