If it had just been LHO, I would be quite prepared to dismiss all the various conspiracy theories as nonsense. The moment Jack Ruby came into the picture and killed LHO, all of that changed irrevocably.
My favorite hypothesis remains that the Ruskies are somehow involved, and there was (inconclusive) evidence known to the Warren Commission, but it was decided that to make this publicly known would have probably ended with WWIII. It is not inconceivable that Nikta Khruschev's ouster was one consequence, as a secret ultimatum might have been delivered to the USSR demanding this as one of several conditions for our keeping this thing secret.
LBJ, after retirement, once leaked to Cronkite that he thought Castro had it done. I don't think you'll get much argument that the Warren Commission's primary purpose was to convince everyone that the now-dead Oswald acted alone because it 1) it exonerated Washington for having done nothing to stop the murder and 2) halted pressure that might have led to military conflict with either Russia or Cuba and a potential nuclear showdown.