But it's not about energy... Either way you go from lotsa velocity to zero velocity.
OK, I said things wrong.
The energy from head motion can be absorbed in the skull and brain - or in the helmet. If none is absorbed by the helmet, the head (and helmet) will rebound more off the ice, at about the same speed, so the final velocity is not zero, so you get a larger velocity change. The force on the outside of the skull is the same, but it lasts twice as long, and can do more damage. Inside the head, depending on the relative timing of the rebound and the brain collision(s), you either get a larger velocity change and force on the brain, or more collisions of the brain with the skull. Either way, you get more damage.
If you see a numeric model of head damage that doesn't take head rebound into effect, it is obviously incorrect.
(BTW, an energy absorbing helmet would also reduce whiplash, because the soft body probably absorbs more energy and rebounds less than the more rigid head.)
An energy absorbing helmet can be much less thick to cushion the collision the same amount. Energy absorption should be a very important component of helmet design.
In terms of physics, it's the difference between a mostly elastic collision and a non-elastic collision. The more elastic collision can do much more damage to the structure of the colliding objects, because of the larger delta V.
I believe this is part of why bicycle and climbing helmets often use a crush-able foam - though such helmets are only good for one collision. And why construction and caving helmets often use suspension systems, which absorb energy by permanently stretching a strap. But they can't take many collisions either.
It's also part of why cars are designed to absorb collision energy in their front ends. The zone of the most severe damage includes the front end, but doesn't extend into the passenger compartment. And you get less rebound if the vehicles stick together. (But, yes,
, cars can't take many collisions either, without substantial repair.)
I believe that skating helmets should be designed to take multiple falls (and hits, for hockey players), because most skaters take multiple falls (and hits). But you need a helmet that is much thicker to meet that requirement, because the obvious ways to design such a helmet absorb little energy.
I'm not sure if you can design an energy absorbing helmet that can take multiple collisions. An elastic closed cell foam absorbs very little energy, because the air compresses and expands outwards again almost adiabatically (without heat loss), and without structural or chemical change, after the collision. But crush-able foam and permanently stretched straps would be damaged by the collision, and lose future effectiveness. Do you know of an energy absorbing material that isn't damaged?