i don't think any kind of head protector would help much.
those scrum caps in rugby are for keeping one's ears on, also to protect the scalp from cuts and abrasions.
if you imagine some eggs in a box. if you wrap that box in bubble wrap then drop it on the ground, it is quite likely the eggs will break.
similarly it is the movement of the brain inside the skull, being bashed against it, and twisting, that causes the damage.
that is why some people think the use of helmets in amateur boxing can be a negative, as it increases the target area ie makes one's head wider, so easier to hit, and the referred jolt to the brain is as bad as to an unhelmeted head.