Maybe I have a more plausible explanation:

You have a humanoid robot with a flywheel parallel to the ground for a head. You want him to move forward. To move forward, force is applied by the robot's feet to the ground. This is not happening at the robot's center of mass, so torque is applied to the system. This torque needs to be matched by the flywheel. Maybe that dynamic causes resistance of lateral movement.

Airplanes and cars would be mostly exempt because their flywheels don't have much angular momentum, and their torque is overcome in other ways. Airplanes would be doubly exempt because their lateral force is applied near their center of mass.

I don't really know anything, and that might have been totally wrong.

On the point-by-point:

- Earth's surface and orbit are not inertial frames due to the rotation. Lateral motion on earth's surface also implies rotation, as it is a sphere. If the robot wanted to travel 12k miles in any direction, it would need to overcome a half rotation of its flywheel. Also it would constantly want to fall down as the earth rotated.

- I just meant the inertia from the flywheel's mass alone. Unless my model above is correct, I agree the mass spinning shouldn't make any difference.

- I agree pivoting about the vertical axis is the most obviously important rotation for bipedal motion. But I think the tilt-starts and tilt-turns might be an important part of bipedal motion as well. Since all the transational force is originating at the feet, you need some way to overcome that torque. You can do it by tilting the center of mass in to the direction of travel, or try to compensate with a flywheel, or maybe attach a propeller to the robot's nose.