Why would Intelligence be interested in faking a serial killer? Simple: to create instability and fear. This was one of the prime goals of Intelligence at the time, and of course it still is.

In the 1960's, the FBI had COINTELPRO and the CIA had CHAOS, and both programs have been partially declassified now, enough so that we know the one of the directives of each program was destabilization.

And this was not just destabilization of the “enemy.” This was a general destabilization of the whole society. Since the entire society was seen to be moving left in the 1960's, the FBI and the CIA felt that general destabilization was necessary to maintain control.

Of course they had been creating fear since the end of WW2, but that was mainly to keep military expenditures high. They needed to justify continued military spending, as well as spending to expand Intelligence, and the best way to do that was to manufacture conflict and fear.

The Cold War was manufactured by both sides, since it allowed for massive “defense” budgets both here and in Russia. The Red Scare in the 1950's was part of that creation of general fear.