This is completely reasonable if your goal is strictly to lower the temperature of the room. But the main reason people use a fan is to have it blowing on you, regardless of temperature. A fan can’t make a hot room cool under any circumstances (by itself), but it can make you feel cool, both psychologically and – if the room is below 110°F or so – by assisting your body’s heat transport.
If you’re leaving a fan on in an empty room then the advice in the OP is correct (though don’t expect miracles), but if you’re in the room then you’re better off doing exactly what you think you should and blasting yourself with the fan.
