Because feathers work better. Using feathers results in higher arrow velocities, greater stability, better guidance, higher accuracy and more forgiving flight. This means less mass to accelerate and less energy wasted. Feathers typically save 40 grains over plastic. Second, feathers produce less friction as they travel over the arrow rest or other bow parts.
Less friction means higher speed.
Third, the superior guidance of feathers prevents yawing and fishtailing of the arrows. Yawing and fishtailing add drag and slow arrow speed. At all normal hunting ranges, feather fletched arrows travel faster, drop less, and arrive sooner than plastic fletched arrows. Further tests by Dave Holt showed that the feather fletched arrow was faster than the identical plastic fletched arrow out to 41 yards. Through out the 61 yard range, the feather fletched arrow arrived at each distance in less time than the vane fletched arrow.