The brilliant part was framing a "communist" or, to be more accurate, a government agent whose job it was to appear as a communist.
Why was that brilliant?
Because this was at the height of the national-security establishment's Cold War racket, when Americans were deeply indoctrinated to hate everything and everyone who was even tangentially related to communists or communism.
Thus, the plotters knew that once it was established that the person who was being accused of the assassination was a "communist," no one would dare come to his defense, given that any such person would immediately be smeared as a "communist lover" or a "communist sympathizer."
That's why it was so essential to develop Lee Harvey Oswald's legend as a "communist" in the months leading up to the assassination.
Prior to moving to New Orleans, Oswald was working at Jaggars-Chiles-Stovall, a photography firm in Dallas that processed film for the U.S. national-security establishment. That's, of course, consistent with Oswald working undercover for the national-security establishment rather than his being a real communist.
Keep in mind, also, that when Oswald returned to the United States after defecting to the Soviet Union and after declaring that he was going to give up U.S. military secrets to the communists, he was not indicted, subpoenaed, questioned, or tortured. That too is consistent with his being an undercover agent posing as a communist, rather than a real communist.