This sounds like a legitimate concern, but I think it depends on the risk of the activity. Do we need to set a good example by wearing helmets as pedestrians and while driving automobiles? Head injuries occur with greater frequency in those activities. While I think the use of helmets by pedestrians would prevent some injuries, it's probably too onerous in practice to adopt it.
I'm aware that cycling without a chin-bar or full-face helmet can result in facial injuries. My childhood friend chipped his two front teeth when he went over the handlebars. But a facial or dental injury is rarely life-threatening. Cycling involves substantial risk of injury to hands, knees, and elbows, but cyclists don't always wear gloves and pads. Again, we often choose to forgo pads because skinning a knee isn't life-threatening. Head injuries are.
The helmet that protects the brain while forgoing protection of the face, jaw, teeth, nose, and sinuses still provides the most critical protection against life-threatening injuries while being the least encumbering. As the risk of more minor injuries goes up with activities like BMX, slope-style courses, or downhill mountain biking, it makes sense to wear additional protection. For a girl riding a cruiser bike on the MUP with streamers on the handlebars? She's better off riding within her ability than being rolled up in bubble-wrap.