Not so "pure and simple" I'm afraid. You will find that what we call ground speed is in effect the first integral of acceleration in a given reference frame which may or may not be physically referenced[*]. What I think you might be thinking of would be the first derivative of change of position over time, which could be a perfectly valid definition (not without its own set of complications, mind you) but unfortunately is not what is used.[*] Consider the following practical example: If you were measuring the ground speed of the Eiffel tower you will find that your answer will be either about zero, or ~3cm/yr, depending on whether you were using the ETRS89 or ITRF2008 reference systems (due to different velocity fields). In other words, even defining what "the ground" is presents a major problem, past a certain threshold of accuracy.
That is ridiculous. The OP was asking groundspeed regarding aircraft in flight. Ground speed is speed traveled over the surface of the earth, at sea level. Please refer to my diagram I drew in a previous post. It is quite simple in this case and there is no need to over complicate it.