Ugh...These theories. In order for something to be self aware it would need to have a soul. The Black Zetsu material is merely Yin-Release that holds Madara's will; think of it as leaving behind something inanimate like a tape recording. This is why Black Zetsu is so mindless and his only purpose is to follow Madara's will. In contrast the White Zetsu were created with Yin-Yang Release and Hashirama's DNA, thus they are living creatures who actually have a will and the fear of death.
To make things simple, you need to look at things from a writer's perspective. If Madara backed up his will inside Obito it would nullify the entire purpose of Black Zetsu, which was to watch over Obito and ensure Madara's plan comes into fruition. Such a silly theory would be anti-climatic and as useless to the story as the Izuna theory.