Is it a plot hole in many Santa Claus movies that no one believes in Santa, yet he turns out to exist in full regalia?

Without discussing too many movies or their intended audience, you know the drill.

Santa doesn’t exist, and everybody knows it, and everybody has evidence that Santa is a fabrication of our culture / society. Anyone who believes in Santa is crazy.

But then, wonder of wonders, Santa does exist, North Pole and all, delivering presents all over the world in one night.

It seems to me that movies should either stick with the Fantasy element that Santa exists and gives presents all over the world, with no help from the adults, OR, the idea that Santa does NOT exist and parents are giving the presents anonymously.

But for Santa to exist when it is established that he does not, seems an inconsistency or plot hole.