If you think that the people not thinking enough are a problem, then you're the poster child of the kinds of issues that arise from someone overthinking things.
The primary reason why we use ceiling fans is because air movement across skin helps increase evaporation
Nope, the primary reason is exactly what you said in the next sentence:
it distributes the air so the overall temperature becomes more uniform
Pretty much any ventilation system, forced air, even open windows, does a poor job of distributing the cooler air throughout a room, especially in houses. So in a very real way it does make parts of a room cooler than they would otherwise be without the fan.
You also seem to be laboring under the assumption that every house in the world is some kind of ideal, perfectly insulating chamber. This is where your overthinking comes in, I assure you that they are not. The miniscule amount of power consumed by ceiling fans (about 50 watts for the average home's ceiling fan at full speed) is dwarfed by the amount of power from solar irradiation and leakage of heat from the outside.
You're correct in the technical sense, which is only the best kind of correct in cartoons.