So if that was the purpose of a conspiracy it failed, so how was Oswald the perfect patsy?
Sometimes good plans fail.
The conventional wisdom was probably that Johnson would retaliate against Cuba or the Soviets if Oswald was linked to the Communists.
It was Johnson who used the possibility of war with the Soviets to convince Earl Warren to join his Commission.
Johnson and Hoover did the unexpected by suppressing conspiratorial loose ends and declaring before all evidence could be analyzed that Oswald acted alone.
His unstable background made the conclusion that he was an unstable character and a lone nut the most likely one surely. An unexplained assassination with leaked evidence of Russian involvement would seem a better approach to me.
You need a fall guy to keep the investigation from taking unexpected turns.