>If I were a surgeon who felt nervous putting a patient on an operating table, the emotion of fear is quite valid in the reasoning to operate

On the contrary, emotion serves as a canary in the coal mine, but you still have to know what killed the canary. It doesn't play a prominent role in the reasoning to not operate, but it does indicate that there is likely a good reason to not operate you still need to identify.

Or, rather, the emotion alerts you to an issue, but you are not going to cancel the surgery and go to your boss or the patient and say "I got a bad feeling about it." You are going to investigate that feeling using reason to find what the true problem is. If, after a thorough investigation involving second opinions, you find nothing to be the problem, you will likely ignore or downgrade your emotional concerns as reason and evidence take clear precedence.

A similar thing arises with your concept of emotion on either side of an argument. It is not working in the same capacity as reason, and thus, is not replacing it (though it may distract). It is useful as a time saving heuristic to mentally debrief and provide your rational mind with a "second opinion" that may catch something it missed. IMHO, this is not a necessary practice in exercising reason, but it is a good practice to engage other parts of your mind to support your reasoning systems as they are anything but infallible.