Most people have no trouble breathing with their eyes closed. If you take a look at "Conscious Breathing" by Dr. Gay Hendricks, "Breath by Breath" by Prof. Larry Rosenberg or "Breath" by James Nestory, you can see that breathing has a special place in addition to its essential role in keeping us alive. When people meditate, they often increase their awareness of what comes to their mind by keeping their attention on a handy anchor and trying to notice when it moves to some topic to think about, such as bills to pay, movies to watch and the experience of their favorite football team. If they catch themselves off thinking about a problem or an experience, they stop that thinking and return to the anchor for their attention.
Since vision is usually our primary sense, the attention anchor may be a spot on the wall or elsewhere. However, eyes can get dry and irritated so the ancients recommended using one's breath as one's attention anchor. Sure, it is easy to breathe consciously and deliberately with closed eyes. Doing that usually has the advantage of increasing one's ability to breathe slowly and fully. Even 3-5 minutes of practice of mindfulness meditating can noticeably increase one's awareness of feelings, ideas and intentions that matter but haven't been getting attention from the boss.