It was a key element of Watchmen. The movie changed the common enemy from aliens, but kept the general concept. It wasn't the governments that created it, but rather the governments were duped into believing it.
Interesting problem in orbital mechanics, suitable for the Musks and Bezoses of the world: calculate parameters for satellite launch, insertion, and stationkeeping needed to simulate seemingly-irrefutable signals from an intelligent ET civilization.
Now there are multiple private teams who could actually pull it off. Or maybe not... I have no idea how hard it would be to make a signal source appear from Earth as if it came from a fixed star, but I suspect it would be extremely difficult to accomplish for any length of time. It's not as if you could just park it someplace. Then there's parallax to consider.
In any event, the message wouldn't be "Build a spaceship with technology no one has ever seen before." The message would be "Get your act together or we'll bulldoze your planet to make room for a hyperspace bypass," or "Take the red pill LOL" or "Get Amazon Prime today. The bargains are out of this world!"
