What physical measurement / elevation is used to define Earth's radius?
Originally, the concept of a reference ellipsoid was an ellipsoid that best approximated mean sea level. This concept predates satellite-based geodesy by hundreds of years. There are now better ellipsoids in terms of providing a better fit to mean sea level than the WGS84 ellipsoid. Yet the WGS84 ellipsoid is used worldwide (including the ridiculously over-precise flattening value).

The WGS84 reference ellipsoid is now just that, a reference ellipsoid (that is, it's the ellipsoid used as a reference by GPS and related systems). In 1993 the WGS84 governing committee voted, with one exception, to retain the 1984 defining values, despite improvements to those defining values. The one exception: The flattening in the original definition of WGS84 was a calculated value, based on the Earth's second dynamic form factor as determined from satellite orbits ($\bar C_{2,0}$ in WGS84, $J_2$ in GRS80). This calculated value became a defining value in 1993. The reason for keeping those older values was GPS. It's better to have a reference ellipsoid that is constant over time than it is to have an ever improving best fit ellipsoid.

Besides, not all of the changes in the best fit ellipsoid represent a reduction in measurement errors. The best fit ellipsoid truly does change over time as the Earth continues to recover from the last glaciation and as the Earth's rotation rate slows down. There are very few applications where a best fit ellipsoid truly is needed while there are many applications where a constant reference ellipsoid is the "best fit".