This kind of charge reveals a good deal about the personality of the people who make it; to impute such motives to another man is to imply you're harboring them yourself.
To those who don't want the truth about Kennedy's assassination to become known, the very repetition of a charge lends it a certain credibility, since people have a tendency to believe that where there's smoke, there's fire.
The CIA could not face up to the American people and admit that its former employees had conspired to assassinate the President; so from the moment Kennedy's heart stopped beating, the Agency attempted to sweep the whole conspiracy under the rug.