I occasionally use a similar online tool, complementary to yours: http://notepad.cc. It stores each note online at its own URL, instead of per-computer at just the root URL. That lets you retrieve and edit notes across multiple computers. I mainly use notepad.cc if I’m using a someone else’s computer or a public computer and want to send some links or a note to myself.
FYI local storage is not reliable, so you may want to think about a fallback, or at least putting a disclaimer explaining that what you write will probably but nitndefinitely still be there when you come back.
Makes sense, and I like the simplicity of the design quite a bit. Maybe one way to augment it would be to add a button that throws the content into a gist/pastebin.something similar, so it could be more easily shared or preserved? Of course, it's a fine line between that and having social media buttons all over.