O doesn't assign utilities to its actions and then choose the best. It chooses its action (by simulating A), labels it with utility 1, and chooses to perform the action it just chose. The last two steps are irrelevant.

"Irrelevant"? If it didin't perform those steps, it wouldn't be a utility maximiser, and then the proof that you can build a utility maximiser which behaves like any computable agent wouldn't go through. Those steps are an important part of the reason for exhibiting this construction in the first place.