When I shoot posed portraits, such as glamour shots and family portraits, my subjects and myself would expect the eyes to be open. I don't know why, but that's how the world functions, so I conform.
When I shoot street candids and adopt reportage/photojournalism style, I am no longer confined by the eyes. The moments I try to capture can be with or without the eye contact. As itoshii mentioned, they simply tell different stories.
If the photographer had managed to establish a direct eye contact with the subject, then the chances are, the subject is aware of the presence of a photographer. The subject's response will be geared by this awareness. The subject would either pose for the camera in some way, or show some unwillingness to be photographed. Either way, the flow of my style is broken. I meant to capture the world pass by with me as a bystander, not in it.
If the eyes are merely opened, and the eye contact is established with someone/something else, that's all it is. They're opened. Whether I want to shoot them open depends on what I want my photo to show. If they're merely opened, as in, not blinking, they play no role in my photo. But if their eyes show emotions, like sorrow, weariness, joy, pain; or if they're looking at something else that's of interest in my photo, then I would want to capture their eyes opened.
The moment that I want to capture can be resting on whether we have open eyes. In candids, it's harder to shoot closed eyes than opened ones. If they're opened, but tell nothing, is there a point to wait for this very long moment? But the expression in this photo, I don't know him, but I classify such an expression as a very hard to come by one. With his head tilted, body angled; changing from one expression to another. This capture is priceless. The eyes shut tells you his expression is changing. It tells you that you had successfully captured a unique moment of his life.
I use how the society behaves to help me understand myself and what I want. I don't use them as chains on my hands when I conform, but as food for thought when I create. I also think whether this society's notion is a sub group, a super ordinate group, or merely a confining narrow perimeter.
One thing for sure, when shooting and viewing candids, the first thing that comes to my mind, is not whether their eyes are opened.
So I'm an outcast and non-conformist. The rest of this society sub-group might see this view as worthless, because it's not representative of the majority. But I hope to raise it anyway, as I don't wish for a future of this subgroup having another set of chains on their hands when they create, but understand the inhibitions that are posed by the notions and perceptions of the larger society.