I don't dispute that you can see more outside the beam of the light if the light is off.
You can see a surprising amount even just by starlight - but I wouldn't want to drive that way, knowing how I've stumbled over things a flashlight would have shown me.
Headlights are definitely to help the driver see (cloudy moonless nights, reflective road signs, etc.). Only at twilight or in fog would they be mostly to help you be seen. When it's really dark, running lights would be sufficient for that.
When you are traveling in the high desert, going without headlights is a great way to see and avoid deer. The deer aren’t going to be dazed by your headlights, and you can see them before they dash out in front of you on the road.
But this isn’t recommended because if another car came along they wouldn’t immediately be able to see you! Light makes you much more visible, and it also allows you to better see a narrow part of the road (more if wide beams are used), but it hides a lot. Of course, being in the high desert in the middle of the night off a freeway, there aren’t many other cars around anyways, if any.