There are hard things inside that shell that can injure a driver's head; in fact, head trauma in car crashes is a huge contributor to automotive deaths.  Helmets would absolutely decrease that (provided they're designed so they don't interfere with the driver's peripheral vision).  There's plenty of data on that.  

The perception is that bicycling requires a helmet due to the lack of a surrounding metal cage, but the data doesn't show that going without is any smarter in a car than on a bike.