Why not? They could get a day off on their birthday since it's a Christmas.
Yeah but then it wouldn't be "your special day". People remember Christmas for someone elses birthday after all. Also, depending on the family and their wealth, would parents bother to get more than the expected number of presents for their child on Christmas because it's their birthday? Not only would the sibling who wasn't born on Christmas day feel chumped for having less number of presents than their Christmas sibling but also be stressful on the parent to get even more presents for their birthday-christmas child.
And you get those relatives who get you the one gift, claiming "This is both your birthday
and christmas gift!" as if to make it sound unique and special when really they just got you the one gift.
I was expected on Christmas Day, I'm glad I postponed for January.