Santa Claus is just a story and people do not even subjectively believe in him (parents pretend to for the sake of their children and once the children are old enough they pretend to for the sake of pleasing their parents and getting candies and presents) and yet he impacts our lives.
That's a very limited perspective of the ways in which people believe in Santa.
In the first place, Saint Nicholas was an actual historic figure, whom Santa is largely, if not mostly, modeled after. Take away the modern American trappings and you still have the European traditions, but underneath all that is an actual historical figure, of importance.
For some, at least, the whole point of Santa is that he is an allegory for charity, and for them that belief in the merit of charity never goes away. When they say, "I believe in Santa," they aren't referring to an old man in a red suit. They are instead referring to that personification of charitable giving around Christmas. Gifts "from Santa" are gifts given anonymously.
Naturally, not everyone thinks in those terms. However, it's disingenuous to focus exclusively on the literals of an old man in a red suit, as if people holding some naive or delusional belief in such a creature, or play acting as if they do, are the only reasons why the rest of the "sane" people must continue to be affected by the notion.
Santa isn't just a story, as you say. It's also a lesson.
