Hello,
I would say that the two important factors that those two exercices reveal are:
1) Speaker placement in your room
2) Acoustic treatment of your room
Those two factors determine the quality of the phantom center that your stereo setup provides.
Headphones eliminate the room acoustics problems, but also substract the ''crosstalk'' and thus eliminate the phantom center.
Acoustic reflections in your room also negatively impact the quality of your phantom center.
So if you would like to improve the quality of the stereo reproducton in your listening spot, place the speakers in a equilateral triangle (with a tape measure, as precisesly as you can) and then add substantial acoustic treatment to your room (that will help greatly with the modal activity, spectral response and RT60).
Hope it helps!