Well we found something we can agree on.
If cycle helmets are for the safety of cyclists then it logically follows that there should be driver/passenger helmets (because serious head trauma happens inside cars all the time), as well as walking down the street helmets and climbing the stairs helmets.
My argument is that a polystyrene lid on your napper isn't likely to make a jot of difference if someone in a lorry runs over your head or a car swerves into you at 40mph, although if you do have a crash, get up, brush yourself off and see that your helmet is smashed your instinct will be "phew, that could have been bad", but there's still a reasonable chance that you wouldn't have hit your head in the first place (as your head is a bigger target with a lid on)