Voltage Divider For DC Fan
First of all, what you have there is not exactly a voltage divider.

You need some power into the motor to keep the fan running, and to beat friction and such, so the motor does dissipate as a resistor, but the equation \$ V = RI \$ is not true for a DC motor.

When you power a motor, at first it is not moving, and the current through it is determined by the winding resistance. As the rotor starts spinning, a new voltage rises: the back EMF. Basically the motor behaves like a voltage source, and its voltage rises until it equals the voltage outside, minus the drop on the winding resistance.

If you put a resistance in series with the external voltage source, the current through it will lower the voltage and the source will appear as a lower voltage source, so the motor will spin slower.

As per your questions, I am not surprised you felt no heat rise. The power dissipated is very low, and unless they used exceptionally small resistors, I expect no significant temp rise.

As per "how do they get away with this"... It's cheap. Like dirt cheap. From idea to gerbers it maybe takes a full hour to do that design.