When a gyro precesses, it takes its spin axis with it and, if you tried to restrain that spin axis somehow, it would create strong torques that could induce secondary precession effects.
When a rotor flaps, the actual spin axis (rotor mast) doesn't move as the blades do - look at introducing a 20 kt head wind gust to a stationary helicopter on the ground, the disc flaps back but nothing else changes - can a gyro do this?