Well, let's say you and I want to secretly exchange stuff nontransparently, but all we have is append only logs. I add a private message to you, to my append only log, that says I'm starting a different append only log. Using that log (only shared between us) we exchange secrets. So everything I publish is completely transparent except for everything that isn't.
I don't think there are any use cases for blockchains. It's just spinning your wheels for what seems like it'd be useful, but there are always better ways to do it.