Reporters (in print) sometimes do that, too.
Mothers of very small children.
I have no idea why we do this. Why* I* do this. It’s only got to confuse the kid learning language, right? But, nonetheless, “Mama’s going to make a bottle.” “Mama’s on the computer.” “Mama’s losing her frickin’ mind!”
Worse, we refer to the tot in the third person instead of second. “Does WhyBaby want some cheese?” “Somebody’s got a dirty diaper! Is it WhyBaby?”
When with another mother/tot dyad, it gets even worse. “Mommy, will you pass Mama a babywipe? WhyBaby’s got schmootz on her face, she does!”
It’s a miracle we ever learn to speak.
More seriously, I wonder if it’s actually required for early language acquisition. I don’t do it every single time, sometimes it’s second person. And, most often, it’s mixed: “Are you thirsty? Do you want some milk? I’ll go get some milk. Mama is making some milk.” Maybe the rephrasing, including changing the point of view, helps kids to learn how to use first and second person. It just seems like there must be some benefit, because it makes no real sense, yet we all do it to little kids.
This isn’t exactly what you’re asking for, but I thought it would be an interesting example. German has an obsolete pronomial usage by which, when directly addressing a social inferior, you would use the third person singular pronoun “Er”, which normally means “he” today. This would be used in cases like someone talking to their manservant. If it was a female servant, I’m not sure whether you still would have said “Er” or “Sie” (which means “she”).
“It puts the lotion on its skin or else it gets the hose again.” 