The problem is that Omega is by definition a hypothetical construct for purposes of exploring philosophical edge cases. We're not talking about any reasonable real-world phenomenon.

Let's taboo Omega. What are you actually describing happening here? What is the entity that can do these things, in your experience? I don't believe your first thought would be "gosh, it turns out the philosophical construct Omega is real." You'd think of the entity as a human. What characteristics would you ascribe to this person?

e.g. A rich and powerful man called O'Mega (of, say, Buffett or Soros levels of wealth and fame - you know this guy is real, very smart and ridiculously more successful than you) shows you two boxes, A and B, and offers you the choice of taking only box A, or both boxes A and B. O'Mega shows you that he has put $1,000 in box B. O'Mega says that if he thinks you will take box A only, he will have put $1,000,000 in it (he does not show you). Otherwise he will have left it empty. O'Mega says he has played this game many times, and says he has never been wrong in his predictions about whether someone will take both boxes or not.

Would the most useful response in this real-world situation be: 1. Take both boxes. 2. Take box A. 3. walk away, not taking any money, because you don't understand his wacky game and want no part of it, before going home to hit the Internet and tell Reddit and LessWrong about it. 4. Invent timeless decision theory?