Your objections are of a different character. Any of these

In the same manner you can "break the problem" by saying "well, what if the players chooses to burn both boxes?" "What if the player walks away?" "What if the player recites Vogon poetry and then shoots himself in the head without taking any of the boxes?"

involve not picking boxes. The issue with the coin flip is to point out that there are algorithms for box picking that are unpredictable. There are methods of picking that make it impossible for Omega to have perfect accuracy. Whether or not Newcomb is coherent depends on your model of how people make choices, and how noisy that process is.