If gyroscopes hold their rigidity in space (which I agree they do in the absence of external forces which is not the case on earth, gravity) and if the earth was flat and not rotating, wouldn’t you expect to see no procession?
If the earth was a rotating globe wouldn’t you expect to see apparent gyroscopic procession the gyroscope remains fixed in space and the earth moves underneath it?
Which of these things do we observe in the real world, procession or no procession?