[freebeard]

I nominate The President's Analyst

The President's Analyst is a 1967 American satirical black comedy film written and directed by Ted Flicker and starring James Coburn, with cinematography by William A. Fraker and a musical score by Lalo Schifrin. The film has elements of political satire and science fiction, including themes concerning modern ethics and privacy, specifically the intrusion of the telecommunications monopoly, working with the U.S. government, into citizens' private lives. The film was released theatrically on December 21, 1967. Although initially not a commercial success, the film was reviewed favorably, eventually achieving cult film recognition.[3]
[snip]
Kropotkin arranges a pickup with his trusted CEA colleague Don Masters, but Schaefer is kidnapped again, this time by TPC (The Phone Company), a far more insidious organization than the FBR or KGB, which had been secretly observing him. Taken to TPC headquarters in New Jersey, he is introduced to its leader, who wants Schaefer's help in carrying out their plan for world domination. As the TPC leader makes his presentation, a camera closeup reveals electronic cables connected to one of his feet, revealing that he is actually an animatronic robot.

TPC has developed a "modern electronic miracle", the Cerebrum Communicator (CC), a microelectronic device that can communicate wirelessly with any other CC in the world. With the CC implanted in the brain, a user need only think of the phone number to be called, and is instantly connected, thus eliminating the need for The Phone Company's massive and expensive wired infrastructure. For this to work, every human being will be assigned a number instead of a name, and will have the CC implanted prenatally. Schaefer is to be forced to assist the TPC scheme by blackmailing the president to pushing through the required legislation. TPC uses a short animated sequence (a parody of the animation in Our Mr. Sun[4]) to explain the plan to Schaefer.

https://www.youtube.com/watch?v=9jEiTxg21q8

edit: What I learned since I posted:

fiscal.thegotham.org: Murder Of A Movie - How J. Edgar Hoover Killed 'The President's Analyst'/

The film was doing well until Hoover saw it. He went ballistic. He sent agents to visit the studio executives and threatened them. He demanded that the movie be removed from the theaters. After realizing how Hoover could hurt them they agreed and the picture disappeared. Then Ted Flicker was black listed and never again made a major Hollywood film.