Why do the semilunar valves not have chordae tendinae?

Pressure: The semilunar valves open and close in response to pressure differentials. Higher pressure in the ventricle forces the valve open and when the pressure drops the valve closes; think of the lid on a trash can as you depress the pedal and you get the idea. The tricuspid and mitral valves require chordae to lock the valves in place so the remain closed when the ventricles generate high pressures.

Not a good answer: You aren't going to like this: it's the way god made them. It is the intrinsic nature of the semilunar valves that they don't have chordae.(it's like asking, why do we have only 2 arms and not 3?).