Surely that’s like what happened in WWI (I think) where they found making soldiers wear helmets created more head injuries than before. They almost stopped using them before realising that less soldiers were returning dead so they just increased medic capacity to handle it.

Wearing a helmet is going to result in a head injury in an accident which would otherwise have caused death.

You probably could use some of the d12 die and just divide the result by 2 (rounding up I suppose) to fill out the missing 4 die.