Morph-X is primarily used in increasing grid energy in your generators/enemy intel. This is essential in progressing through each of the episodes in the main game.
The more grid energy each generator has, the more Morph-X it earns, so it is strongly advised that you increase grid energy on your generators as much as possible.
In events, how much you earn Morph-X will be the basis of your ranking that will determine your final prizes when it ends!