When you get right down to it, why would Michael enter the lion's den just to try and find out who was the traitor in his family? That makes no actual sense (while it may make dramatic sense).

While the traitor remains, Michael is in danger. However, he would have the resources to counter or mitigate that danger. In cuba, he had none of that. He could be murdered at any time by either Roth's minions or Batista's or be held hostage.