Now, I have received back a fourth recently requested death certificate - and this one did include the cause of death. The funny thing? I received two copies: one with the COD and one without. I only paid for one copy. Also, this ancestor died in 1953, the same year that one of the other ancestors died, and who's death certificate did not include COD.
I have to conclude that the GA Vital Records office doesn't know it's own policies! I've sent them an email, enquiring as to their policy on listing causes of death.
Here is the latest one I received, about my Great-Grandmother, Ruby Lee Waters Huyler. She died of "chronic and acute alcoholism." (click for a larger image)