Not quite 'Nanny AI', but a similar idea dates back to D.F. Parkhill (1966, p. 61-62), who imagined a "computer utility" that could sustain a global peace under the United Nations:

The new generation of on-line, multi-user military [computer] systems is rapidly coming to resemble the oft-heralded "total management systems" — an integrated, multi-user, multi-input, display, processing, communication, storage, and decision complex, incorporating in one man/machine package the total operations of an organization...

Such a total military management system is in fact now taking shape in the United States [and] will tied together into one gigantic integrated command and control complex all of the far-flung command-and-control systems of the Army, Navy, and Air Force as well as the information systems of other government agencies such as the Central Intelligence Agency, Stated Department, and Civil Defense organization... Conceivably, the Soviet Union also has her own version of [this] under development; thus it is not inconceivable that in some future more rational world the American and Soviet systems might be connected together into a global peace-control system under the United Nations. [Such a system has] obvious uses in policing an arms-control agreement and controlling the operations of international peace-keeping forces...

In the final chapters, Parkhill seems to have successfully predicted online, automatic banking, the universal encyclopedia, online shopping, and growing technological unexmployment.