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The simple, logical answer is that whichever producer or writer/story editor would have been assigned to this was someone who actually did call her/his father "Daddy" well into their teens.
My friends and I were just like you in that we shifted to "Mom and Dad" somewhere in the middle of grade school, but I am aware that this is not universally donepartly by regions of the country, and partly by individual familiesthe "Daddy" and "Mommy" versions are used until later ages.
It always sounded odd to me when Ricky and David called Ozzie Nelson "Pop," but that had to be what they actually called him, so they used it on the show.
Of course, my suggested answer could be 100% wrong, but it seems likely because if it seemed wrong to the people in charge, they would likely have changed it.