I've always thought the head rests spoil the lines of a Morgan.
I have hacksawed a couple of inches off the end of the metal tube in the past to get them to go down flush with the seat back.
I take them off and store them away and use 2 little plastic plugs that are from an MG to fill the hole in.
I think they're angled way too far back to be of any benefit to reduce whiplash in the event of being rear ended.