But he wanted the world to know that there was a Kira. His ambition was to be the God of the world. He could anonymously send instructions to the world to do what he wanted only if people knew there was a Kira.
Yeah, that would be a strong disincentive to frame the CIA, since his goal morphed pretty early on from fixing the world to becoming a god. For a more prudent and altruistic death note user, that particular strategy could have fit well into the automation idea.