The form of the morph curve does depend
on how the original curves are parametrized.
Changing the parametrization of the original curves does not change their appearance when displayed, but it does change the appearance of the morph curve.
Geometrically, the morph curve is constructed by joining two corresponding points on the original curves by a line, and then positioning a third point at a specific proportion along this line. Drag the middle red dot to see the morph curve change.