You claimed that the only source of drift is friction within the mechanism. But in reality, the amount of drift will be different depending on whether you're flying east/west or north/south, and it differs depending on your distance from the equator. None of that would be true on a flat Earth.

On a flat Earth, it wouldn't matter where in the world you are, which direction you're flying, or even whether the plane is moving or not. The amount of drift would be the same every time because none of those factors affect the amount of friction within the instrument.