They seamlessly integrate the status history as well as letting us easily post to Twitter when there is a problem. They also provide a feed and reliable infrastructure separate from our own that integrates with monitoring tools.
When your app is offline, it's a huge relief to be able to easily update Twitter and have a central location for clear status information without having to go to Twitter and Tumblr or wherever and tie everything together.
It's certainly not cheap, but compared to building, hosting, and maintaining an equivalent service, it's a great deal. Some of their more advanced features, like allowing customers to sign up for text alerts are great as well if you need it.
The service is way more than just a hosted Tumblr account, and I'd definitely recommend them if you're looking for something like this.