It's not just to do with a chepo fan.
The load a fan draws is proportional to the speed at which it is running. Very roughly if you double the speed of a fan, you have to cube the original power requirement for the new fan speed.
Trying to remember back to fluid dynamics 1.01:
power = efficiency * blade area * 0.5 * air density * air velocity ^3
The faster it spins, the greater the mass of air that it has to move. Hence, if you had a 120mm fan that could draw several amps, it would be spinning so fast that you would end up with an airflow cavitation. This in turn would cause a random and variable loading on the fan blades from the airflow variations, which in turn would cause the power consumption to vary. That would lead to random and potentially very excessive torsional loads on the spindle.
That's why if massive volumes of fluids (including air) need to be moved, it is done using very large, slow spinning blades - think big ships and wind turbines.