Do you think that a rule utilitarian could have a better response to this? Because rule Utilitarianism, unlike AU, implies that we should not break certain rules because it would decrease well-being in the long run. So, it would be bad to kill the person because it may result in panic and fear in society.

As for desires, I hold a somewhat different view on the topic. What if, and correct me if I am wrong, we could say that the person does have a desire at the moment they are in coma. Now of course, if they are unconscious, they wouldn't be feeling anything. However, would it not be fair to say that a part of their body is alive and actively desires to be well. Because there is clearly a difference between a person who is totally dead and a person who is in coma. Otherwise, we wouldn't bother trying to save those people. But we know that people can be saved from a state of coma. What would you say?