I've never understood why people even wanted to use this. For the styling? So you can just copy some random stuff from Twitter and it looks like Twitter but is also interactive? Just with the Facebook like-Button, you're exposing your visitors to the tracking of Twitter. For what? Just so you can quickly copy one snippet and be done with it, instead of manually copying author name, content and link and spending 10 se…
It's very convenient (just click share or use a WordPress widget to embed tweet), it always look pretty, and there are multiple actions available from the tweet: go to profile, reply, share ...
So more features for less time to set-up. This is a service like all other Service, you usually tradeoff something like privacy for convenience. Why use Dropbox when you can have your own NAS ?