AerocatS2A
To test your theory let’s consider two altitude such that the still air at the higher altitude must move twice as fast as the still air at the lower altitude, so that both parcels of air remain stationary relative to the ground. (I know that the atmosphere isn't really thick enough for this, but it is only the geometry that matters)
Now let’s imagine that we have two aircraft, one at each of the two altitudes, hovering in this still air, such that in each case their TAS is zero.
After 1 hour the earth will have rotated through 15 degrees. The two parcels of air and the two aircraft will have moved through the same 15 degrees to remain over the same point on the ground. But the inertial distance moved by the higher aircraft will be twice that moved by the lower aircraft. You theory is good so far.
Now lets set both aircraft to be flying in the direction of earth rotation at a TAS of 10 knots. After one hour the earth and the air will have rotated through 15 degrees. The lower aircraft will have moved through 15 degrees plus whatever angle equates to 10 nautical miles at that altitude. The higher aircraft will also have moved through 15 degrees plus whatever angle equates to 10 nautical miles at that higher altitude.
But the angle equating to 10 nautical miles at the lower altitude will be greater than the angle equating to 10 nautical miles at the higher altitude. In this case it would actually be twice as much. So the lower aircraft will have moved through a greater angle and a greater distance over the ground.