The standard reply to your objection is that Newcomb’s Problem doesn’t actually care about the “ritual of cognition” that you happen to use. It only cares about your answer. You could one-box because you worship Cthulhu, instead of EDT, and still win. For example, I don’t subscribe to EDT, but still one-box because I find UDT’s solution convincing :-)
The standard reply to your objection is that Newcomb’s Problem doesn’t actually care about the “ritual of cognition” that you happen to use. It only cares about your answer. You could one-box because you worship Cthulhu, instead of EDT, and still win. For example, I don’t subscribe to EDT, but still one-box because I find UDT’s solution convincing :-)