As the only purpose for ground speed is for navigation in relation to the Earth's surface, ground speed must surely by speed over that surface. If the extra "circumferal" distance you are flying is significant enough to reduce that speed, then that correction must also be taken into account when navigating.
Lets say you are "flying" in a space shuttle at an altitude of 320 km - you work out the horizontal component of your velocity (in relation to the Earth's centre) as a groundspeed and then plot that distance over an hour across a surface map. Will you be anywhere near over the position you have plotted? Then it's not groundspeed, is it?