I was thinking of something like that, but wanted to make the use case as general as possible so people can decide how they want to use it. Maybe I'm wrong :S
I don't know about the technical solutions, but the way Branch currently integrates with Twitter, the way you can be conversing on Branch and still your conversation spills over Twitter...is what I have in mind in terms of this type of simple blogging service. The paragraph or couple of sentences should spill over to Twitter, and/or the Tweets should spill over to this type of service. All this not necessarily in a way it is currently setup by other platforms (like Wordpress, you can cross-post blogs to Twitter) but something naturally with least effort and distraction.
Am I making sense? There may be some services out there providing this experience, but ... anyways.