Why are the antennas in space wave mode of propagation generally mounted at heights of many wavelengths above the ground?
space waves are used for the line of sight (LOS) communication.
For LOS communication the antennas are kept heights of many wavelengths above the ground because the direct waves get blocked at some points due to the curvature of the earth.
So to receive signal beyond the horizon, receiving antenna must be high enough to intercept the LOS waves.