Do you ride in urban traffic? Or do serious running?
I can only speak about my own experiences. When I'm running, if my mind wanders I slow down, or lose my stride, or have more risk of turning an ankle. I try and remain focused - this enhances my breathing, helps me maintain my stride with a good consciousness of what's happening in my hips (given that I am no longer young), and also helps me maintain control and recover if I feel my ankle start to move in a way that it shouldn't.
When I ride, I am not subconsciously thinking about the vehicles around me. I am conscious of them. Extremely so! (This is why I am worried about electric vehicles. Obviously I have no objections to a reduction in emissions, but I'm worried that I won't be able to tell when an electric vehicle is close to me.)
As I've said, I am not a fighter. I don't know how melee combat works. But I would expect some of the basic elements of the experience, its relationship to perception of the environment and control of the body, etc, to broadly resemble what I am familiar with. Like running, fighting involves deliberate and atypical physical exertion. Like cycling in urban traffic, it requires attention to and response to risk that presents itself rapidly and as not fully subject to one's control.
I find it hard to believe that it is rote, or subconscious, in the sense that the fighter is thinking about other things while fighting and just acting "automatically".