Well, I've fallen off bicycles when I was a kid dozens of times, scraping off several yards of skin - I had no helmet.

I've fallen off and lost all the skin off the side of my face and broken my arm - not even a headache.

Bicycle helmets are NOT designed for solitary falls, but relatively major accidents, such as where a car hits you from behind.
The car hits you at about 25km/h (after braking), forcing you forward at a fast rate straight into the ground.
Your head impacts the ground relatively close to vertical (compared to a solo fall), the styrofoam impacts and absorbs energy - preventing the brain from being sloshed around to much, and preventing skull creep, where the skull creeps back on the spinal column and the brain fluid crushes the brain.

BTW, a skull fracture can be good, since it allows cranial fluid out preventing brain damage from skull creep. An impact hard enough to fracture the skull will not be protected by bicycle helmets.
But this is a large impact, rare, and will usually result in spinal damage anyway.

A helmet will NOT protect the face, scalp, or hair style.