Perhaps keep the face covered somehow, with goggles or a visor, but make the helmet more like wrestling helmets, to protect the soft areas of the skull.
For some people, since their head is already so soft, they still need the helmet.
OBTW, this is a stupid, stupid idea. Instead of getting rid of helmets, more technology should be used to make them safer and prevent neck and brain injuries. I am sure we could be doing more in these areas. Why did neck rolls ever disappear from the game? Why not have a more dynamic version of the HANS device used in NASCAR developed? Sure, it couldn't and shouldn't look and act just like the HANS unit, but perhaps share some it's theory...